Banks are generally open weekdays 9am-noon and 2pm-5:30pm. Larger banks don’t close for lunch. Some are open on Saturday mornings.
MANY GUIDEBOOKS SAY that you can get a cash advance with your Visa or Mastercard directly from the (human) teller at most banks, just bring your passport for ID. I HAVE NEVER FOUND THIS TO BE TRUE (and trust me, I’ve tried). A few French banks will exchange money (again, most don’t unless you’re a client of that bank), but they will not perform any other operations for non-account holders. They will tell you to use the automated cash machines.
Post offices also handle basic banking transactions and Western Union transfers. The best place to pick up your Western Union transfer is at La Poste (which is also a bank in France) at 52 rue du Louvre (1st, M° Louvre-Rivoli or Les Halles). Even though this post office is open 24/7, the Western Union window (on the left when you walk in) is only open 8am until 6pm on weekdays, and 8am until 11:30am on Saturdays. Don’t forget your ID and the Western Union code (which the sender of the transfer should give you).