The Federal Courts in New Orleans seemed to frequently change both names and locations. Here is a list for what we now call the U.S. District Court, Eastern District of Louisiana:
1812 - 1823: 269 (now 919) Royal Street
1823 -1847: old United States Custom House (across from present site, corner of N. Peters & Canal)
1848 - 1850: 427-33 Royal Street
Early 1850's: Gallier Hall
Late 1850's - 1861: Merchants Exchange
1861 - 1865: Merchant's Exchange/ The Presbytere
1866 - 1915: U.S. Custom House and Post Office
1915 - 1963: U.S. Post Office and Courthouse
1964 - 1976: 400 Royal Street
1976 - now: Hale Boggs Federal Building-Courthouse on Poydras
A guide to federal courthouses in New Orleans by the United States District Court, Eastern District of Louisiana
U.S. Court of Appeals for the Fifth Circuit convened for the first time on June 16, 1891, in the U.S. Custom House and Post Office. In 1915 the Court moved to U.S. Post Office and Courthouse on Lafayette Square. In 1994 the building was renamed the John Minor Wisdom United States Court of Appeals Building.