Thanks, everyone, for the suggestions. I'll check those films out.
It's not terribly important that I find a film like the one I described. It's just that I heard a radio commercial the other day that used voice over with sexy sax music to depict a stereotypical film noir scene, and it got me to thinking that I don't actually know a film noir film that observes those characteristics. It's been a while since I've seen it, but I think Tension (1949) might have the sexy sax solos I'm looking for. I'm not sure about the voice over narration.