<?xml version="1.0"?>
<ownershipDocument>

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2013-11-19</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0001580156</issuerCik>
        <issuerName>Houghton Mifflin Harcourt Co</issuerName>
        <issuerTradingSymbol>HMHC</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001300714</rptOwnerCik>
            <rptOwnerName>Anchorage Capital Group, L.L.C.</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>610 BROADWAY</rptOwnerStreet1>
            <rptOwnerStreet2>6TH FLOOR</rptOwnerStreet2>
            <rptOwnerCity>NEW YORK</rptOwnerCity>
            <rptOwnerState>NY</rptOwnerState>
            <rptOwnerZipCode>10012</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
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            <isTenPercentOwner>1</isTenPercentOwner>
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            <officerTitle></officerTitle>
            <otherText></otherText>
        </reportingOwnerRelationship>
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    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001300711</rptOwnerCik>
            <rptOwnerName>Anchorage Advisors Management, LLC</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>610 BROADWAY</rptOwnerStreet1>
            <rptOwnerStreet2>6TH FLOOR</rptOwnerStreet2>
            <rptOwnerCity>NEW YORK</rptOwnerCity>
            <rptOwnerState>NY</rptOwnerState>
            <rptOwnerZipCode>10012</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
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            <officerTitle></officerTitle>
            <otherText></otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001300650</rptOwnerCik>
            <rptOwnerName>Davis Anthony Lynn</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>610 BROADWAY</rptOwnerStreet1>
            <rptOwnerStreet2>6TH FLOOR</rptOwnerStreet2>
            <rptOwnerCity>NEW YORK</rptOwnerCity>
            <rptOwnerState>NY</rptOwnerState>
            <rptOwnerZipCode>10012</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
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            <officerTitle></officerTitle>
            <otherText></otherText>
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    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001300710</rptOwnerCik>
            <rptOwnerName>Ulrich Kevin Michael</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>610 BROADWAY</rptOwnerStreet1>
            <rptOwnerStreet2>6TH FLOOR</rptOwnerStreet2>
            <rptOwnerCity>NEW YORK</rptOwnerCity>
            <rptOwnerState>NY</rptOwnerState>
            <rptOwnerZipCode>10012</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
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            <isTenPercentOwner>1</isTenPercentOwner>
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            <otherText></otherText>
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    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001300713</rptOwnerCik>
            <rptOwnerName>Anchorage Capital Master Offshore, Ltd</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>610 BROADWAY</rptOwnerStreet1>
            <rptOwnerStreet2>6TH FLOOR</rptOwnerStreet2>
            <rptOwnerCity>NEW YORK</rptOwnerCity>
            <rptOwnerState>NY</rptOwnerState>
            <rptOwnerZipCode>10012</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle></officerTitle>
            <otherText></otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock, $0.01 par value per share</value>
            </securityTitle>
            <transactionDate>
                <value>2013-11-19</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>1717309</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>12</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>15830831</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                    <footnoteId id="F1"/>
                    <footnoteId id="F2"/>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>By Anchorage Capital Master Offshore, Ltd.</value>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock, $0.01 par value per share</value>
            </securityTitle>
            <transactionDate>
                <value>2013-11-19</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
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            <transactionAmounts>
                <transactionShares>
                    <value>44659</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>12</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>409795</value>
                </sharesOwnedFollowingTransaction>
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            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                    <footnoteId id="F1"/>
                    <footnoteId id="F2"/>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>By Anchorage Illiquid Opportunities Offshore Master, L.P.</value>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock, $0.01 par value per share</value>
            </securityTitle>
            <transactionDate>
                <value>2013-11-19</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
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            <transactionAmounts>
                <transactionShares>
                    <value>14886</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>12</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>136598</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                    <footnoteId id="F1"/>
                    <footnoteId id="F2"/>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>By Anchorage Illiquid Opportunities Offshore Master II, L.P.</value>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock, $0.01 par value per share</value>
            </securityTitle>
            <transactionDate>
                <value>2013-11-19</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
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            <transactionAmounts>
                <transactionShares>
                    <value>67820</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>12</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
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            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>622320</value>
                </sharesOwnedFollowingTransaction>
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            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                    <footnoteId id="F1"/>
                    <footnoteId id="F2"/>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>By Anchorage Illiquid Opportunities Offshore Master III, L.P.</value>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock, $0.01 par value per share</value>
            </securityTitle>
            <transactionDate>
                <value>2013-11-19</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
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            <transactionAmounts>
                <transactionShares>
                    <value>82344</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>12</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
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                <sharesOwnedFollowingTransaction>
                    <value>755590</value>
                </sharesOwnedFollowingTransaction>
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            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                    <footnoteId id="F1"/>
                    <footnoteId id="F2"/>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>By GRF Master Fund II, L.P.</value>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock, $0.01 par value per share</value>
            </securityTitle>
            <transactionDate>
                <value>2013-11-19</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
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            <transactionAmounts>
                <transactionShares>
                    <value>14684</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>12</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>134740</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                    <footnoteId id="F1"/>
                    <footnoteId id="F2"/>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>By PCI Fund LLC</value>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock, $0.01 par value per share</value>
            </securityTitle>
            <transactionDate>
                <value>2013-11-19</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>P</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>3500000</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>12</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>19330831</value>
                </sharesOwnedFollowingTransaction>
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            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                    <footnoteId id="F1"/>
                    <footnoteId id="F2"/>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>By Anchorage Capital Master Offshore, Ltd.</value>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <derivativeTable></derivativeTable>

    <footnotes>
        <footnote id="F1">Anchorage Advisors Management, L.L.C. is the sole managing member of Anchorage Capital Group, L.L.C., the investment advisor to each of Anchorage Capital Master Offshore, Ltd., Anchorage Illiquid Opportunities Offshore Master, L.P., Anchorage Illiquid Opportunities Offshore Master II, L.P., Anchorage Illiquid Opportunities Offshore Master III, L.P., GRF Master Fund II, L.P., and PCI Fund LLC. Mr. Davis is the President of Anchorage Capital Group, L.L.C. and a managing member of Anchorage Advisors Management, L.L.C. Mr. Ulrich is the Chief Executive Officer of Anchorage Capital Group, L.L.C. and the other managing member of Anchorage Advisors Management, L.L.C.</footnote>
        <footnote id="F2">Each reporting person disclaims beneficial ownership of the reported securities except to the extent, if any, of its or his pecuniary interest therein, and this report shall not be deemed an admission that such reporting person is the beneficial owner of the reported securities for purposes of Section 16 of the Securities Exchange Act of 1934, as amended, or for any other purpose.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>Anchorage Advisors Management, L.L.C., By: /s/ Kevin M. Ulrich, Authorized Signatory</signatureName>
        <signatureDate>2013-11-21</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>Anchorage Capital Group, L.L.C., By: /s/ Kevin M. Ulrich, Authorized Signatory</signatureName>
        <signatureDate>2013-11-21</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>/s/ Anthony L. Davis</signatureName>
        <signatureDate>2013-11-21</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>/s/ Kevin M. Ulrich</signatureName>
        <signatureDate>2013-11-21</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>Anchorage Capital Master Offshore, Ltd., By: /s/ Natalie Birrell, Director</signatureName>
        <signatureDate>2013-11-21</signatureDate>
    </ownerSignature>
</ownershipDocument>
