1. You just need the medical associated with your licence - i.e. the FAA medical must be current - and your licence must be current and valid in all other respects.
2. You must fly within your own licence privileges and observe the laws of the land you're in - i.e. when in Rome,......
3. Sorry - forgot about the '2 out of 3' rule!
4. Don't forget that many small aerodromes may not have fluent English speakers on the RT. This is particularly true in France.