In an age when zydeco is dominated by boys only a few years removed from their first shave and senior prom, Goldman Thibodeaux, 70, ranks as a newcomer, too. Thibodeaux had never even held an accordion when he bought his first instrument at age 52.

Thibodeaux’s only CD, Les Miseres Dans Le Coeur (Miseries of the Heart) on Louisiana Radio Records, which he made with now-deceased fiddler Calvin Carriere, is only three-years-old. Thibodeaux’s skills are new, but his sound re...