Back in 1986, when BeauSoleil was first starting to tour a lot outside Louisiana, back when the Doucet brothers still had a bit of hair atop their heads, the band played at the Kennedy Center, Washington’s red-carpeted bastion of high culture. BeauSoleil was just a quartet in those days—Michael Doucet on fiddle, David Doucet on acoustic guitar, Errol Verret on accordion and Billy Ware on triangle and rubboard—and when the four musicians looked out over the East Coasters sunken in their seats,...