However, there are other actresses named Renee who might fit the "old-time" bill, depending on what you consider "old-time":
* Renee Asherson: A British actress who was active in the 1930s and 1940s.
* Renee Adoree: An American actress who was popular in the 1920s.
Do any of these names ring a bell? Let me know if you have more clues about the actress you're looking for!