Are you expecting all inclusive? That can be hideously expensive so I would bin that idea for a start, you can save so much that way.
I would be weighing up what my priorities were in your list. If your top priority is nice weather guaranteed you're going to have to consider certain parts of France and the possibility of driving there ((with perhaps a cheap stay overnight on the way) You could go on the shuttle as that's often cheaper than the ferry, and exciting for kids - they like the novelty of sitting in their car on a train. Once you've narrowed it down to there, you have to decide if being by the sea is essential for your kids' enjoyment. We can get drawn into thinking that a holiday has to be a certain way for it to be a "proper" holiday, but we've found that to not be true. There are lakeside beaches in France with watersports etc.
Next, is kids' entertainment a real priority? If it really is (and personally I don't think it's essential for children to be able to enjoy themselves), then you're looking at considering a holiday park. But you'd probably have to compromise on the standard of accommodation you're used to. If you decide that organised entertainent ISN'T essential then you could consider nicer smaller gite complexes where there are likely to be other children for yours to play with. They tend to have nicer, prettier and more relaxing for adults shared pools than the overcrowded ones at holiday parks. Most have games rooms, playgrounds, trampolines etc. Most kids love the freedom of making new friends at these sort of places and going off to play table tennis with them or a game of football etc.
We could never afford holidays abroad when the kids were little so went to Devon or Cornwall. After one terrible holiday in a Haven where we thought "never going to a holiday park in the UK again! Not even for the kids' sake!", we had a few successful holidays on non working farms in Devon or Cornwall with groups of self-catering cottages with shared pools and indoor and outdoor play facilities, animals, sometimes organised activities etc. When they outgrew those we just rented extra nice cottages or apartments in picturesque towns and villages by the sea.
But to be honest, after one too many weeks where we had rain and miserable grey skies every day, not being able to use the nice garden or balcony we'd paid for, no barbecuing etc, and rip off entries to museums etc to try to fill the time, we looked to France instead and wished we'd done it sooner! We loved the Dordogne - perfect for kids of age 8 ish and up. Loads of stuff to do, absolutely loads, in certain parts. I'm not very sporty but canoeing on the Vezere or Dordogne rivers is very pleasant and gentle indeed. It's gorgeous weather. Very pretty everywhere. Loads of prehistory stuff everywhere, plus castles, adventure parks, really great.