There’s a reason you will likely hear “Walking to New Orleans” more than once during this year’s Jazz Fest. Fats Domino’s 1960 top-10 pop hit evokes the desire to come back home to the Crescent City better than any other song. And for the thousands who were flushed out of town by the Army Corps of Engineers’ failed levees, the sing-along refrain echoes their own longing to return.

At first listen, the song sounds like a simplistic blues, but on closer inspection it reveals itself as a mira...