The production company was aided greatly in its ability to film in and around New Orleans by the state's Film Commission. Shortly after this film (which is about political corruption) premiered, several members of the Film Commission were indicted in a kickback scandal.
Jim Garrison, the judge in Remy's bribery case, is an actual lawyer and judge who worked in New Orleans. He was, for a time, the city's district attorney. A case he had while in that position was the subject of Oliver Stone's film JFK (1991). Garrison was played by Kevin Costner.
Reportedly, star Robert Redford has said that he literally dragged British producer David Puttnam, who was the CEO of Columbia Pictures at the time, to a screening of the film at the Sundance Film Festival. Afterwards, Puttnam then picked-up the picture for distribution.
The signature New Orleans setting was actually a late change in the development of the film. The original title of the script was Windy City, and set in Chicago. The change in location is attributed to a suggestion by then Production Executive Ken Aguado, who was a recent graduate of Tulane University.
According to the Wikipedia website, "the producers used well-known locations [in New Orleans, Louisiana, USA] such as Tipitina's, Antoine's, Blaine Kern's warehouse full of Mardi Gras parade floats, and a French Quarter strip joint, to flesh out the mood of the film."
Mel Gibson, Harrison Ford, Bruce Willis, Richard Gere, Michael Keaton, Alec Baldwin, Gary Oldman, Liam Neeson, Bill Paxton, Kevin bacon, Tommy Lee Jones, jeff bridges, Sean penn, Michael Nouri, Kurt Russell, Patrick Swayze, John Travolta, Mickey Rourke, Arnold Schwarzenegger, and Sylvester Stallone were considered to play Lt. Remy mcswain.
This cinema film was made and released around just four years after a tele-movie which had the same name which was The Big Easy (1982). Both titles involved crime and were set in the city of New Orleans in Louisiana, USA.
The trivia item below may give away important plot points.
While the UK theatrical release ends with the boat exploding, a fade out and cutting to Remy and Anne dancing around on their wedding night, the UK video release has an extra scene which features Anne talking Remy out of resigning and Remy proposing marriage.