As a none eat meater myself I find that when I am in France there isn't such a large choice of veggie dishes as the UK though it is improving and I always managed to find something tasty. Last time I stayed in Paris it was also near the Eiffel Tower I can't remember any restaurant names but did find that lots of places had delicious omelettes with mushrooms or cheese, lots of place serve Pizza with veggie options and I found an Indian restaurant near the Ecole Militaire metro stop (the other end of the park behind the tower) which had the usual meatless options.

Lebanese restaurants also serve delicious vegetarian dishes. To find out any local to the Eiffel Tower, you might google 'Restaurants Vegetariens Paris' and of course Indian and Chinese/Vietnamese restaurants should also offer tasty meals. Unfortunately, as Judith points out, the French tend to be a nation of meat eaters! Bon appetit!

When i was in Paris I ate mostly in creperies - it's still authentic French food, but there's lots more vegetarian options than in a normal restaurant, and as it's all put together right there you can request dishes without the meat.

My wife is vegetarian and the one thing the french really don't understand is 'vegetarean'. Even a sald is difficult for them. You just end up with a plate of leaves ...

But that's what a salad is to your average Frenchman. Salade verte = leaves with vinaigrette! If you want a salad with other bits in, you should ask for a Salade Compose (pronounced com-po-zay).

Other useful terms for a vegetarian:

oeuf dur - hard boiled egg
fromage - cheese
tofu - tofu
champignons - mushrooms
poivrons - green peppers

je suis vegetarien(ne), je ne mange pas de viande.
Je ne mange ni du poisson ni de la viande - I eat neither fish nor meat.

Hope this helps.