With Pets, you may prefer Backstreet Bistro, as I understand they have an outdoor patio that IS pet friendly. But as another responder has mentioned, Cuistot is a French fine dining restaurant. I wonder if you'd be welcome with your French Poodle or French Bulldog?
It's a fine dinning establishment, i'd call to make sure but I would say they only allow service animals. They do have outdoor seating which might be more lax.
Thanks! Your answer is awaiting moderation.