Q. What Year did the State of Louisiana require its citizens to produce a photo ID when voting at the polls? Which was the first election in which this

Good Question.  This rule is governed by the Revised Statutes RS 18:562.  I've included that below, and you can look it up on the Louisiana State Legislature Laws Index.  Section 562 was first enacted in 1976 and has been revised many times since.   1976 was a Presidential Election year, which Jimmy Carter won against Gerald Ford.
 

§562.  Prerequisites to voting

A.  Identification of voters.

(1)  A person who desires to vote in a primary or general election shall give his name and address to a commissioner, who shall announce the applicant's name and address to the persons at the polling place.

(2)  Each applicant shall identify himself, in the presence and view of the bystanders, and present to the commissioners a Louisiana driver's license, a Louisiana special identification card issued pursuant to R.S. 40:1321, or other generally recognized picture identification card that contains the name and signature of the applicant.  If the applicant does not have a Louisiana driver's license, a Louisiana special identification card, or other generally recognized picture identification card that contains the name and signature of the applicant, the applicant shall sign an affidavit, which is supplied by the secretary of state, to that effect before the commissioners who shall place the affidavit in the envelope marked "Registrar of Voters" and attach the envelope to the precinct register, and the applicant shall provide further identification by presenting his current registration certificate, giving his date of birth, or providing other information stated in the precinct register that is requested by the commissioners.  However, an applicant who is allowed to vote without the picture identification required by this Paragraph is subject to challenge as provided in R.S. 18:565.

B.  Review of precinct register.  The commissioners shall then determine:

(1)  If  the applicant's name is found in the precinct register on the official list of voters and he has not voted absentee by mail or during early voting, one of the commissioners shall announce the applicant's name again.

(2)  If the applicant's name is found in the precinct register on the inactive list of voters and has not voted absentee by mail or during early voting, the applicant may vote after complying with provisions of R.S. 18:196(B).  After such compliance, one of the commissioners shall announce the applicant's name again and shall preserve the address confirmation card received from the voter by placing the address confirmation card in the envelope marked "Registrar of Voters" and attaching the envelope to the precinct register.

(3)  If the name of a qualified voter was omitted from or incorrectly printed on the precinct register, the commissioner shall:

(a)  Contact the registrar of voters to ascertain whether or not the person applying to vote is registered to vote in that precinct.

(b)  In the absence of a valid challenge of the voter, allow the applicant to sign an affidavit before a commissioner attesting that he is a qualified registered voter and describing the error or omission in the voter records.

(c)  Preserve the applicant's original affidavit as part of the election records by placing it in the envelope marked "Put in Voting Machine" and place the duplicate affidavit in the envelope marked "Registrar of Voters" and attach the envelope to the precinct register.

C.  Handwritten signature of the applicant.  If the applicant is able to sign his name, he shall sign his handwritten signature in ink in the space for his signature on the precinct register.  When the applicant has submitted picture identification to the commissioners, the applicant's signature shall be compared to his signature on the picture identification.  If the applicant is unable to sign his name, he shall make his mark in ink in the proper space on the precinct register.

D.  Procedure after identification.  If satisfied that the applicant has identified himself as the voter named on the precinct register and that he is qualified to vote, a commissioner shall initial the precinct register opposite the voter's signature or mark.  The voter then shall be allowed to vote.

Acts 1976, No. 697, §1, eff. Jan. 1, 1978.  Amended by Acts 1977, No. 523, §1, eff. Jan. 1, 1978; Acts 1980, No. 506, §1, eff. Jan. 1, 1981; Acts 1986, No. 669, §1; Acts 1988, No. 909, §1, eff. Jan. 1, 1989; Acts 1993, No. 418, §1, eff. Jan. 1, 1994; Acts 1994, 3rd Ex. Sess., No. 10, §1, eff. Jan. 1, 1995; Acts 1997, No. 779, §1; Acts 1999, No. 254, §1, eff. Jan. 1, 2000; Acts 2001, No. 1032, §7; Acts 2001, No. 1181, §1, eff. Jan. 1, 2002; Acts 2005, No. 220, §4, eff. Jan. 1, 2006; Acts 2007, No. 240, §1; Acts 2009, No. 369, §1.

NOTE:  See Acts 2001, No. 1032, §17.