As long as the dogs are kept away from the table I'd far rather have them than badly behaved children racing around while the parents sit eating and drinking totally oblivious to their little darlings upsetting everyone else.
By the way, I was guilty of this in France myself once but soon taught my toddler son to stay at the table until we'd finished, then take him outside to play. Took toys to keep him occupied but you can't spend the afternoon sitting chatting and drinking with children. It isn't fair on them or other diners
You probably can with a dog if it's had a good walk first, it'll just snooze under the table.