i've stayed in the Briancon area twice in the last 2 years. both times we ended up in the campsite in L'Argentiere. the campsite is right beside the slalom course just as you leave town. L'Argentiere is just down the road from Briancon. the campsite there was full of paddlers every time we were there (in June) and there is a really cool little island you can go party on, so you don't disturb everyone else on the site and get kicked out!
we also spent a few days at a campsite about a mile outside of Briancon. more of a family place (ie no other paddlers) but it had a swimming pool. they weren't too impressed with the amount of noise we made but it was a nice change. a bit more expensive though.
there are also a couple of campsites in the Embrum direction if you wanna stay closer to the wave there. or you could rent a house in Brincon itself, but i've never done that so i don't know much about it.