Solomon Burke’s soul classic “Cry to Me” inspired Marc Broussard’s eighth album, S.O.S.: Save Our Soul 2. Broussard’s studio interpretation of “Cry to Me”—and his choice of his father, guitarist Ted Broussard, as a session player—says much about the 34­-year-­old Cajun soul singer from Carencro.

“Cry to Me” is one of the soul standards that Broussard, this year’s headliner at the Bogalusa Blues & Heritage Festival, grew up loving in southwest Louisiana.

“Solomon was such a ...