Good evening,
This is the difference between France and, it seems, the United States, for example.
In France, a minor who resides there must present an authorization to leave the country if they travel without either of their legal guardians.
If they travel with one of their legal guardians—so, with you—they don’t need to present anything. And if the other guardian had reasons to oppose the trip, they would have to go to court, prove it’s for a valid reason, and have it noted on the passport.
https://www.service-public.fr/particuliers/vosdroits/F1359You don’t need to worry unless your child’s father takes legal action to get a travel ban. You have the right to take your child to the UK without them being held hostage by their father.
That’s why I think—and this is just my personal opinion—that the rights and freedoms of minors are much better protected in France than in the United States or Canada, among others.
Have a good evening.
Michel