It's a beautiful name that has never been overused, at least not in the USA (not sure about France). But trust me, it's not always an easy name to live with. People spell it wrong on a daily basis. A lot of people don't even know how to pronounce it when they see it written out. But the worst thing is RENE... That is for the male spelling. Hate to burst bubbles but it's true.
Various misspellings I have encountered: Reene, which shouldn't be pronounced like Renee Rena, Renea, Renae, Rennee, Renne, Rene, Reena, Reenae. They are all wrong. Most of those are different names all together!
Renee of France (1510-1574), youngest daughter of King Louis XII of France and his wife Anne of Brittany. She later married Ercole II d'Este and had 5 children with him.