The series just had a theme.
..by Paul Sawtell, which sounded nothing like this.
As you can see from the cover art, this is definitely from the movie. And Bobby Darrin sang it.
Frankie Avalon sang it (and he was in the movie). I didn't think there was any doubt it was from the movie. Bobby Darrin sang "La Mer" aka "Beneath the Sea". I don't know if he ever did a version of this tune. If he did, I want it.