Feldman served as a law clerk to Judge John Minor Wisdom of the United States Court of Appeals for the Fifth Circuit from 1957 to 1959.

[3][4] Feldman was among seventy-one Jewish delegates (prior to his conversion to Roman Catholicism) and alternates to the convention.

He was confirmed by the United States Senate on October 4, 1983, and received his commission the following day.

[8] On September 3, 2014, Feldman issued a ruling upholding Louisiana's ban of same-sex marriage.

Feldman also equated the recognition of marriage without regard to sex to incest, writing that he was concerned that recognizing marriage without regard to the sex of the members of the couple would lead to a slippery slope that would eventually require courts to recognize polygamy and incest.

All such unions would undeniably be equally committed to love and caring for one another, just like the plaintiffs.Lawyers for the plaintiffs immediately announced plans to appeal the ruling.

[12] A federal judge is required to consider recusal when he owns shares in one of the parties in the case before him, however none of the companies listed in Feldman's 2008 disclosure were directly involved in the action against Salazar.

[14] As of the June 9, 2010 amended complaint, Transocean, Black Rock, BP, and Exxon-Mobil were not plaintiffs in the action.

[15] On August 17, 2020, Feldman ruled that Louisiana's bar closures due to the COVID-19 pandemic are constitutional.