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

    <schemaVersion>X0303</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2009-08-17</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0001089819</issuerCik>
        <issuerName>CLECO CORP</issuerName>
        <issuerTradingSymbol>CNL</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001186052</rptOwnerCik>
            <rptOwnerName>GARRETT J PATRICK</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>P.O. BOX 5000</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>PINEVILLE</rptOwnerCity>
            <rptOwnerState>LA</rptOwnerState>
            <rptOwnerZipCode>71361-5000</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle></officerTitle>
            <otherText></otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Common Stock, $1.00 par</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>50110.383</value>
                    <footnoteId id="F1"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
    </nonDerivativeTable>

    <derivativeTable>
        <derivativeTransaction>
            <securityTitle>
                <value>Phantom Stock</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <footnoteId id="F2"/>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2009-08-17</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>427</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>24.21</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <footnoteId id="F2"/>
            </exerciseDate>
            <expirationDate>
                <footnoteId id="F2"/>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock, $1.00 par</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>427</value>
                    <footnoteId id="F2"/>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>46165.866</value>
                    <footnoteId id="F3"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">Includes 106.872 shares acquired through the Cleco Corporation Dividend Reinvestment Plan on May 20, 2009.</footnote>
        <footnote id="F2">The shares of phantom stock relate to dividend reinvestment on shares of phantom stock pursuant to the terms and provisions of the Cleco Corporation Deferred Compensation Plan (the &quot;Plan&quot;).  The reporting person has elected to defer receipt of these shares under the Plan.  Each share of phantom stock is the economic equivalent of one share of Cleco Corporation common stock.  Shares of phantom stock may be transferred by the reporting person into an alternative investment account in the Plan at any time pursuant to the terms and provisions of the Plan.</footnote>
        <footnote id="F3">Includes 6,007 shares of phantom stock (not subject to restrictions) related to dividend reinvestment on shares of phantom stock pursuant to the terms and provisions of the Plan.  Includes (a) 1,200 shares of phantom stock subject to restrictions that lapse on July 23, 2010; (b) 2,339 shares of phantom stock subject to restrictions that lapse on January 28, 2011; (c) 1,064 shares of phantom stock subject to restrictions that lapse on July 22, 2011; (d) 2,228 shares of phantom stock subject to restrictions that lapse on January 27, 2012; (e) 1,846 shares of phantom stock subject to restrictions that lapse on January 26, 2013; (f) 2,140 shares of phantom stock subject to restrictions that lapse on January 25, 2014; and (g) 2,544 shares of phantom stock subject to restrictions that lapse on January 30, 2015.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>Judy P. Miller, Atty-in-fact for J. Patrick Garrett</signatureName>
        <signatureDate>2009-08-18</signatureDate>
    </ownerSignature>
</ownershipDocument>
