I'm a french vegetarian living in France after living 6 years in Scotland, France is years behind on the diet inclusion issue, I was shocked how difficult it was to find a place to eat out in Paris, way too many cafe/restaurant/etc.. gets defensive and refuse to serve you if you don't have the "historical diet" (whatever that means) of france, and a lot of them don't offer any "common alternative diet" options on the menu. And it's not better outside of Paris.
Then of course there are some great places that try to include everyone regardless of their diet, and they are increasing in numbers, but they are still the exception rather than the norm which is a shame.
If you ever goes in Paris and looking for a fully vegetarian classy restaurant, I recommand "Polichinelle", it's a bit on the expensive side (~50 euro/person), but it's high level cuisine, and for a special occasion it's really worth it.
Never been to Italy, but I expected it would be even worse over there, Italians are often very invested in their opinion about food😄 some of my Italian friends can spend the whole meal debating about what they are eating