In the state House under the administrations of Governors John McKeithen and Edwin Edwards, Brinkhaus served on CODOFIL, in which capacity he received the L'Ordre de la Pleiade for his work in promoting French language and culture. On August 19, 1972, having earlier in the year taken the oath of office for his second term in the Louisiana state House, Brinkhaus ran in the Democratic closed primary, prior to the establishment of the Louisiana nonpartisan blanket primary system, for Louisiana's 8th congressional district seat, since disbanded. He polled 31,934 votes, but victory went to former U.S. Representative Gillis William Long of Alexandria, who finished with 61,452 votes. Another contender was Democratic state Senator J. E. Jumonville, Sr., of Ventress in Pointe Coupee Parish. Long then reclaimed the seat by defeating in the general election held on November 7, 1972, the American Independent Party choice, Dr. S. R. Abramson of Marksville in Avoyelles Parish and the Republican Roy C. Strickland, then of Gonzales in Ascension Parish. Brinkhaus chaired the Senate Education Committee and was a major promoter of his alma mater, the University of Louisiana at Lafayette. He authored legislation to establish special protection for school teachers facing acts of violence from their unruly pupils. His law created the crime of assault of a school teacher with an enhanced penalty. Brinkhaus worked to provide low interest loans for the purchase of school buses and greater operational allowances for bus drivers. He worked for increases in pay for teachers and support personnel as well as for additional supplements to retired educators. He led the effort to require that a teacher evaluation plan be developed by local school boards, rather than the Louisiana Department of Education. Senator Brinkhaus also served at various times on the Senate Finance, Judiciary, and Agriculture committees. He sponsored legislation to halt the distribution of campaign contributions to legislators within the Louisiana State Capitol, the governor’s mansion, or any other state office building. He voted to require the disclosure of certain expenditures by persons who lobby the legislature and to require that individual legislators disclose the receipt of gifts of transportation, food, lodging, or entertainment. After five terms in the state Senate, Brinkhaus lost his bid for reelection in 1995 to the Republican Tommy Casanova, a Louisiana State University football legend. Casanova polled 21,543 votes to Brinkhaus's 15,793. Casanova then vacated the seat after one term. In addition to his legal practice, Brinkhaus was affiliated with Marta C Turksel Educational Consulting, location not specified. Brinkhaus created the Dr. Armand L. and Julia Thoms Brinkhaus Fund to benefit the Dupre Library at the University of Louisiana at Lafayette. On November 7, 2009, the Acadian Museum in Erath inducted Brinkhaus into the "Order of Living Legends." One of Brinkhaus' brother-in-law was the Republican state Representative Roderick Miller of Lafayette, whose term extended from 1966 to 1968, when Miller was defeated by Edgar G. "Sonny" Mouton, Jr., for a seat in the state Senate. Miller's second wife was Brinkhaus' sister, Anna Jane Gaiennie Miller.