I moved out of the country but I'm originally from Paris. I hope I can help.
In the last few years, Paris has improved in terms of veganism, you'll find great restaurants! What sort of restaurant are you looking for? You'll find all sorts: snacks, burgers, chinese, pizza, traditional, "gastronomic", etc.
The following website may be useful. It's in French but you have a map with all the vegan-friendly locations in Paris. It's pretty exhaustive and up-to-date. http://vg-zone.net/vg-carte-de-paris/
You may find it difficult to go to omni places and ask for vegan options, few will have some or even try to be accommodating, but you can always try. I've had nice surprises. Veggie restaurants and places will usually be more helpful with regards to veganising their meals.
In terms of finding vegan products in shops, you will but they're usually quite expensive and not very good to be honest. The last time I went there a couple of months ago, I've seen some had started to offer Alpro products but it's not that common in France yet. If you want an extensive range of products, try health shops, they're called "magasins bio" (literally organic shops in you don't speak French). Not cheap either but you'll find better choice and quality.
Finally, for the most extensive vegan range of products, there's this one all-vegan shop near place de la République, called Un Monde Vegan. You'll find any vegan product you want from seitan, to cheese and pizzas. http://www.unmondevegan.com/index.cfm