Yes, they are, if that's what they insist on - but surely most (if not all) restaurants have a vegetarian dish or two on the menu as long as they eat fish.
There is a local place, famed for its pies, mostly meat but 2 are fish-based and one vegetarian (out of about 40 pies, but still, they are there).
Veggies have a really tough time in France and have to just accept that a lot of restaurants say 'non' when asked about a veggie option. I remember going in a group which included a couple of v's - the restaurant (asked in advance) were happy to include a suitable dish. It turned out to be beautifully cooked and presented bundles of haricots and asparagus - fastened together with strips of bacon and fried in duck-fat!!! V's ate it anyway, unpicking the bacon with good-humour. :)