Oh dear.. the words "Foodies" "Best places" and "toddler" do not go together , at least not in France.
Most restaurants do not open for dinner till 7-730, and dinners regularily take several hours.
Children are seen and not heard , no one would think it was ok for your child to wander about in a restaurant.. or even a brasserie or café.. French children are not allowed as a rule.. child centric parenting isn't really a thing in Europe.. lol
I think you may have to wait a few years for some real foodie dining out experiences with your child.
The other option is to stay in a very nice hotel that provides a babysitting service.. I was a bit of a nervous nelly that way and didn't leave my kids with hotel sitters till they were quite a bit older .. like 9 or 10 though.
Or bring your parents! lol ( hey we've did that once.. on a cruise, baby was too young for sitting services )
There is however one thing you can do.. which is enjoy really amazing fresh food you purchase and prepare yourselves.. and things like cheeses , pates, rillettes, charcuteries goods, you can visit bakeries and get a special treats, and of course purchase some wine .
A one bedroom apartment where you can put your tot down to bed and then still have a space to socialize .
There really are little parks all over the place.. so perhaps just focus on a few things.
Get an apartment with AC , and if not.. make sure its on a bottom floor.. with good ventilation so you can open windows.. and that you are on a quiet street as if you have to have windows open you don't want street noise. Really though.. get ac.. and its not easy to find btw.. and make sure apartment SAYS they have an elevator .. as if they don't specify it.. don't assume they have one. Also... the first floor in France is our second floor.