I lacked confidence in my French and thus missed some opportunities to dine in restaurants or visit wine bars where I would have been called on for something more complex than "Je voudrais une tranche de cette quiche, s'il vous plait" or my absolute favorite, "Un comme ça, s'il vous plait." (That's one reason I want to go back, so I can build my language skills and try out more of the food and wine on offer.) Still, I had some excellent restaurant meals, which I obtained by a combination of using what French I had and pointing at the menu. I had some great salads and omelets, and I noticed that ham seems to play a crucial role in many dishes. I read online that you can find vegetarian food fairly easily in Paris, but if you are asking whether a salad includes meat, you need to ask about ham specifically, as Parisians will sometimes describe a salad as meat-free even if it contains ham. Evidently ham is not always considered meat. I find this a somewhat sympathetic viewpoint; for years I have joked that pepperoni is not a meat but a condiment. At any rate, although I generally do not eat meat, I ate plenty of ham in Paris, and it ranged from OK to very good. Paris might be navigable for a vegetarian, but in my experience, being a vegan would take a fair amount of work. Most of my bakery take-out meals were either sandwiches with cheese on them (my favorite was a baguette with fresh mozzarella, tomato, and basil at the Tuileries Gardens) or quiches of all kinds, which of course contained eggs and cheese.
Regarding the menu: You must remember to call it "la carte," because "le menu" is typically a set course of dishes at a fixed price, which might or might not be what you're after. In my experience, it does not hurt to ask specifically for the menu after you are seated. One of the more perplexing moments in dining was at a place near the Musée d'Orsay. I think people stopped in there for drinks alone as well as for meals, which we did not grasp right away. We seated ourselves, and when the waiter came to our table, there was a moment of awkward silence until he asked, "Vous voulez manger?" We hadn't realized that it wasn't obvious that we were there for lunch, and were briefly taken aback by the question, but managed to say that yes, we wanted to eat.
I bought my wine at the Monoprix, which had a small selection of bottles out on shelves in the regular grocery area but also had a little cave, or wine cellar. I enjoyed everything I bought there. I also gazed into the windows of the wine shops, but never did go into one. Next time.
Language was really not all that much of a barrier when it came to food. It is worth noting that I experienced absolutely no rudeness. If you start out with your best French, at least a hearty "Bonjour, madame" or "Bonjour, monsieur" and as much French as you can muster thereafter, my experience is that people will meet you at least halfway. I have to admit that I didn't always get what I expected, especially when asking for bread, but I liked everything I got. And how often can you say that?