As for France, nos special requirements https://www.service-public.fr/partic...osdroits/F1359. Kids travelling with a national ID (without a passport) used to need an "autorisation de sortie du territoire", but it's not longer required, and most probably it applied only to French citizen (and maybe residents).

And as stated above, wives keep their maiden name on French IDs and passports, but can add a "nom d'usage" that is usually their husband's name or a combination of their maiden and their husband's name, however they don't have to, and they can do at any time. Furthermore, more than half of first-born children in France are born out of wedlock, so the name on the passport shouldn't be a big issuee.
For peace of mind, I'd bring a copy of the adoption papers, though..