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

    <schemaVersion>X0303</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2010-08-05</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0000886206</issuerCik>
        <issuerName>FRANKLIN COVEY CO</issuerName>
        <issuerTradingSymbol>FC</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001017012</rptOwnerCik>
            <rptOwnerName>WHITMAN ROBERT A</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>2200 WEST PARKWAY BLVD</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>SALT LAKE CITY</rptOwnerCity>
            <rptOwnerState>X1</rptOwnerState>
            <rptOwnerZipCode>84119</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>Chief Executive Officer</officerTitle>
            <otherText></otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>common shares</value>
            </securityTitle>
            <transactionDate>
                <value>2010-08-05</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>4700</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>6.2573</value>
                    <footnoteId id="F1"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>2136700</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <derivativeTable></derivativeTable>

    <footnotes>
        <footnote id="F1">The price reported in Column 4 is a weighted average price.  These shares were sold in multiple transactions at prices ranging from $6.20 to $6.385, inclusive.  The reporting person undertakes to provide Franklin Covey Co., any security holder of Franklin Covey Co., or the staff of the Securities and Exchange Commission, on request, full information regarding the number of shares sold at each separate price within the ranges set forth in this footnote to this Form 4.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Stephen D. Young, Attorney-in-Fact</signatureName>
        <signatureDate>2010-08-06</signatureDate>
    </ownerSignature>
</ownershipDocument>
