There are already two different threads running on that topic (one vegetarian, one vegan), but then for Paris only.
It may be a bit more difficult in Biarritz, especially if you don't eat seafood.
The typical southwestern food is pretty much meat based (confits, foie gras, etc.).
As for Bordeaux, I'd imagine, you should be able to find vegetarian restaurants. Lots of people, especially young ones over here, aren't that much into meat anymore (especially true for red meat).
Also, I think the French are pretty inventive when it comes to non-meat dishes. It's a lot more than just salads, omelettes, etc.
You may want to have a look at the two existing threas here:
http://bonjourparis.ipbhost.com/index.php?showforum=38And I agree with Karen. Also, it's not that difficult to find dishes without any meat or fish at lots of restaurants.