Davis was in private practice in New Orleans from 1960 to 1964, and then joined a law firm in New Iberia, where his partners were Congressman Pat Caffery and U.S. Circuit Judge John Malcolm Duhé, Jr.
President Ronald Reagan nominated Davis to the United States Court of Appeals for the Fifth Circuit on November 1, 1983, to a seat vacated by Judge Robert A. Ainsworth Jr., who died on December 22, 1981. Reagan at first considered Ben Toledano, a New Orleans lawyer and former Republican political candidate for the slot but withdrew the nomination after opposition surfaced from the NAACP. Davis was again confirmed by the United States Senate on November 15, 1983, and received his commission the following day.[2] He assumed senior status on December 31, 2016.[2]
Judge Davis was appointed by Chief Justice William Rehnquist as a member of the Advisory Committee on the Federal Rules of Criminal Procedure on October 1, 1995. Davis became Chairman of this Committee on October 1, 1997 and served as Chairman until October 2001 when his term of service ended.
In 2014, Judge Davis received the prestigious American Inns of Court Professionalism Award for the Fifth Circuit at the American Inns of Court Celebration of Excellence held at the Supreme Court of the United States. Judge Davis was inducted into the Tulane Law School Hall of Fame in March 2015. In 2017, the Louisiana Bar Foundation awarded Davis its Distinguished Jurist Award.
Notable cases
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In 2022, Davis dissented from the Fifth Circuit's decision in Securities and Exchange Commission v. Jarkesy in which the majority found the SEC's administrative enforcement against Jarkesy to be unconstitutional.