When Cher brings her Here We Go Again Tour to New Orleans on December 13, she’ll be in the hometown of the musician who helped make her 55 years of stardom possible. Harold Battiste Jr. arranged Sonny and Cher’s biggest hits of the 1960s. In the ’60s and ’70s, Battiste put his jazz career aside while he worked as the duo’s musical director and conductor.

Battiste met Sonny Bono in Los Angeles in 1956, when they were both working for Specialty Records. In his memoir, Unfinished...