"Swamp Music?" Do you perhaps mean "Cajun Music?"
When I played on Bourbon Street, we were in the middle of what was referred to as the "British Invasion" - with the Beatles, the Rolling Stones, the Animals, Herman's Hermits, Petula Clark, Joe Cocker, ... that bunch. We played "Brit Rock" and a lot of Deep South Rhythm & Blues.
The French Quarter has changed a lot since my college days, but there are still a few musical holdouts here and there. I haven't been down there in a long time. Some of the places I played are still there but under new management. Others have been repurposed into restaurants or from "pure" bars to bar & grill establishments. I wouldn't know my way around any more.