Le Procope is the oldest café in Paris, founded in 1686! Wow! Nowadays it's more of a swanky restaurant, and along with being the oldest café around it's also known for being a place where tons of famous historical dudes hung out. Seriously, just about anybody you can think of from French history and literature and philosophy frequented the Procope: Voltaire, Rousseau, Balzac, Victor Hugo, and even some Americans like Benjamin Franklin and Thomas Jefferson. (I wonder if the French rolled their eyes at how touristy the place was getting). Voltaire still has a table at the Procope that remains perpetually reserved for him. Weird, but I like it.
The Procope is a bit pricey, but absolutely worth it for the experience. The decor is gorgeous, and it's definitely worth exploring the place a bit on your way to the restrooms (which, incidentally, are marked Citoyens and Citoyennes, i.e. male and female citizens of the republic). Reservations are recommended, as the place gets crazy, especially on weekends. No worries, the front desk will be able to help you in English.