Great advice from Bestaunt about restrooms, and that applies to big people as well as little ones! We take the opportunity to use them whenever those opportunities present themselves, whether we think we need to or not. Some of them may require a small payment so keep a stash of coins on you at all times.
In both Paris and Italian cities, the bars and cafes are good sources if willing to make a small purchase...which we do as businesses often have signs on the restroom doors stating that their facilities are only for patrons. The facilities in Italian cafes/bars/restaurants are often down a steep flight of stairs, in the basement, so can be interesting to track down!
But the good news is that children are rockstars in Italy. Wee folks are welcome almost anywhere and can attract lots of kindly attention! Where we'll order a coffee or whatnot in a bar/cafe before hitting the loo, a frantic mom with a tot who needs to go NOW need not waste time and won't be expected to. I would expect the same to be true in Paris.
Oh, and don't avoid bars in Italy. They're as much coffeeshops as places to consume alcohol, and are very family friendly. Most carry Italian sodas, ice cream and other treats for the younger set. :O)