Geez, Dick, the song was about events in 1814/15, and written in first-person. The lyrics should be expected to reflect how a veteran of that battle might have spoken.

Anyway, there are still folks around the South who pronounce the word "master," especially when used in direct-address, as "marse." Nowadays, of course, the term is more likely to be used ironically than straightforwardly.

The lyric starts out saying "in 1814 we took a little trip," but the battle actually took place in January of 1815. It was part of the "War of 1812," and actually occurred after the treaty had been signed, unbeknownst to the participants. I'm not sure of the exact date, but I know that the annual anniversary reenactment just took place within the past week or so. The site was (and is) just outside the City of New Orleans, in Chalmette, St. Bernard Parish, site of some of the worst flood damage when the levees failed in 2005.