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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2019-12-13</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0001071236</issuerCik>
        <issuerName>RED RIVER BANCSHARES INC</issuerName>
        <issuerTradingSymbol>RRBI</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001770154</rptOwnerCik>
            <rptOwnerName>Salazar Tammi R.</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>1412 CENTRE COURT DRIVE, SUITE 402</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>ALEXANDRIA</rptOwnerCity>
            <rptOwnerState>LA</rptOwnerState>
            <rptOwnerZipCode>71301</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>See Remarks</officerTitle>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>COMMON STOCK</value>
            </securityTitle>
            <transactionDate>
                <value>2019-12-13</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>5</transactionFormType>
                <transactionCode>G</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F1"/>
            </transactionCoding>
            <transactionTimeliness>
                <value>E</value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>600</value>
                    <footnoteId id="F1"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0.00</value>
                    <footnoteId id="F1"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>38050</value>
                    <footnoteId id="F2"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeHolding>
            <securityTitle>
                <value>COMMON STOCK</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>34250</value>
                    <footnoteId id="F3"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>By Spouse</value>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">This is a voluntary filing to disclose a transaction involving a bona fide gift of securities.  Price is not applicable to dispositions resulting from bona fide gifts.</footnote>
        <footnote id="F2">Includes 2,260 shares of unvested restricted stock granted to the reporting person which vest as follows: (i) 810 shares vest on July 1, 2020, (ii) 610 shares vest on July 1, 2021, (iii) 440 shares vest on July 1, 2022, (iv) 280 shares vest on July 1, 2023, and (v) 120 shares vest on July 1, 2024. The reported shares of unvested restricted stock are subject to forfeiture upon the occurrence of certain events specified in the restricted stock grant.</footnote>
        <footnote id="F3">Includes 2,260 shares of unvested restricted stock granted to the reporting person's spouse, Bryon C. Salazar, which vest as follows: (i) 810 shares vest on July 1, 2020, (ii) 610 shares vest on July 1, 2021, (iii) 440 shares vest on July 1, 2022, (iv) 280 shares vest on July 1, 2023, and (v) 120 shares vest on July 1, 2024. The reported shares of unvested restricted stock are subject to forfeiture upon the occurrence of certain events specified in the restricted stock grant.</footnote>
    </footnotes>

    <remarks>Executive Vice President - Red River Bank Private Banking, Mortgage, and Investments</remarks>

    <ownerSignature>
        <signatureName>/s/ Amanda W. Barnett, as Attorney-in-Fact</signatureName>
        <signatureDate>2019-12-18</signatureDate>
    </ownerSignature>
</ownershipDocument>
