Hi Margaret
Many of the campsites on the Ile de Re would satisfy your criteria.
The island is cyclist's paradise as it is criss-crossed with a VERY extensive network of cycle tracks including ones to the beaches.
When we were there in 2008 the weather was warm and sunny but there was often a pleasant sea breeze to balance this out a little.
We stayed at Camping Providence at the far end of the island from the bridge. It was not the most polished of campsites and very French but we enjoyed our fortnight there. We can read my reviews of the site and general comments on Ile de Re on the (1)caravantalk website
http://www.caravantalk.org.uk/topic/20611-france-poitou-charantes/
or
(2) ukcampsite.co.uk website. Sorry I can't give the exact link for the latter as my ukc account is playing up at the moment. If I remember correctly the ukc campsite search section, also, has reviews for other Ile de Re Campsites.
In fact, come to think, I believe that the Ile de Re has a website listing all of its campsites - can't remember the link but you could probably google it if interested.
We generally liked Ile de Re VERY MUCH. Some interesting towns and villages, good beaches and everything one could want for a holiday. The road access for caravan is good although of course one does has have to pay the toll for the bridge to cross onto the island, it's free to leave!!! We did not leave the island during our fortnight's stay as there was plenty to occupy us and several supermarkets, etc for shopping.
Regards
Tim