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

    <schemaVersion>X0304</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2012-02-27</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0001347815</issuerCik>
        <issuerName>Flagstone Reinsurance Holdings, S.A.</issuerName>
        <issuerTradingSymbol>FSR</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001411821</rptOwnerCik>
            <rptOwnerName>WATSON PETER F</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O FLAGSTONE REINSURANCE HOLDINGS SA</rptOwnerStreet1>
            <rptOwnerStreet2>65, AVENUE DE LA GARE</rptOwnerStreet2>
            <rptOwnerCity>LUXEMBOURG</rptOwnerCity>
            <rptOwnerState>N4</rptOwnerState>
            <rptOwnerZipCode>L-1611</rptOwnerZipCode>
            <rptOwnerStateDescription>LUXEMBOURG</rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle></officerTitle>
            <otherText></otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable></nonDerivativeTable>

    <derivativeTable>
        <derivativeTransaction>
            <securityTitle>
                <value>Restricted Share Units</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>0</value>
                <footnoteId id="F1"/>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2012-02-27</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>4885</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                    <footnoteId id="F1"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <value>2012-02-27</value>
                <footnoteId id="F2"/>
            </exerciseDate>
            <expirationDate>
                <footnoteId id="F3"/>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Shares</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>4885</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>19151</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">Each Restricted Share Unit (&quot;RSU&quot;) represents the right to receive, without payment to the Company, one newly issued, fully paid and non-assessable common share of the Company, subject to the terms and conditions of the RSU Plan and grant certificate evidencing each grant.  In the discretion of the Compensation Committee, upon exercise, the RSU grant may alternatively be paid in cash, or partly in cash and partly in common shares.</footnote>
        <footnote id="F2">The RSUs vest 100% on the date of the grant.</footnote>
        <footnote id="F3">The RSUs have no expiry date.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ William F. Fawcett by power of attorney</signatureName>
        <signatureDate>2012-02-29</signatureDate>
    </ownerSignature>
</ownershipDocument>
