Yvonne (played by Madeleine Lebeau) was in Rick’s before Ilsa (Ingrid Bergman) showed up. She approaches Rick and they have the following conversation:
Yvonne: Where were you last night?
Rick: That was so long ago I don’t remember.
Yvonne: Will I see you tonight?
Rick: I don’t plan that far ahead.
She turns and orders a drink from Sasha, but Rick tells her she’s had enough to drink and has Sasha take her home.
Renault sees the exchange and comments that Rick is careless in tossing away women and they he (Renault) may go pay her a visit.
Through that scene, we can infer that Rick and Yvonne had recently been lovers and that Rick, for whatever reason, had broken it off.
That Yvonne had dabbled elsewhere during their liason. Otherwise, why would Rick have given her up? It’s more in what she did than in being beautiful, and I refuse to believe that the latter was the reason.
That is an inference I never saw the many times I’ve watched the movie. I thought she was just a one night stand. That’s why Renault said he tosses women away.