We have been in June and December.
We prefer December because it is a chance to get away from the cold and also time to relax before the craziness of the season.
Everything is open and we find the water comfortable. Some villas start their high season prices December 1st others start on Dec. 15th. We select a villa based on the latter. A few times we had to pay a higher rate for 1 or 2 nights as we were renting past the 15th but overall was within the budget.
We bounce around the island a lot. I would guest about 25% of our stays have been on the Dutch side and 75% of the French side.