1. Who are the best to talk to while crossing water?
It's not a matter of who's best to talk to, but who you must talk to. Look at your chart and think FIR boundaries.
2. Is it true I have to talk French on Sundays?
No.
3. Is it advisable to go on a Sunday?
No reason why not except that it will probably be very busy in the town. It used to be the most popular day for GA pilots from the UK; not sure if it still is.
Although it's an easy trip, it involves more thorough planning than just asking here. Plan very thoroughly, and get a FI or experienced pilot to check your plan.
If you're renting, the school probably has restrictions which may involve having to do the trip with an instructor first.
You'll need to file a Flight Plan - and close it after each leg. If you can, get hold of a form and fill in the basics in advance to save time on the day. It's a little complicated until you get used to it.
Check the weather very carefully to make sure you'll be able to get back. In marginal visibility, a grey sky meeting a grey sea has it's own very real hazards.
If you like fish, go to the Restaurant-Perard in the centre of Le Touquet. It doesn't look anything special but the fish is fresh and delicious. Their home-made fish soup is the best I've tasted in Europe.