I first heard this song when Jo Stafford covered it in the ‘50s. IIRC the Hank Williams version was used in the sound track of The Last Picture Show.
As for the dish, Jambalaya, I remember having it in New Orleans. It was highly seasoned and I enjoyed it. Crawfish Pie is what it sounds like. Gumbos are stews that traditionally are thickened with either okra, or, as in the song, file, which is sassafras powder.
What this has to do with accordions I can only guess.