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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2019-07-01</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

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

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001770010</rptOwnerCik>
            <rptOwnerName>Carriere Isabel V.</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>2019-07-01</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F1"/>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>600</value>
                    <footnoteId id="F1"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0.00</value>
                    <footnoteId id="F1"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>38680</value>
                    <footnoteId id="F2"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">Reflects 600 shares of unvested restricted stock granted to the reporting person on July 1, 2019 that will vest in equal installments on each of the first five anniversaries of the grant date. 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="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>
    </footnotes>

    <remarks>Executive Vice President, Treasurer, Chief Financial Officer and Assistant Secretary</remarks>

    <ownerSignature>
        <signatureName>/s/ Amanda W. Barnett, as Attorney-in-Fact</signatureName>
        <signatureDate>2019-07-02</signatureDate>
    </ownerSignature>
</ownershipDocument>
