Yes, it would certainly need all paperwork plus proof of a rabies shot and be muzzled in public. I've been delving further and there seems to be such a Catch 22 situation that several sites advise against bringing any category 1 or 2 dog into France, even for a week's holiday.
The Catch 22 is a UK owner (I'm just using UK as an example) can have all the paperwork up to speed but it's not French paperwork. In France owners of a Cat 1/2 need the registration card (or ID card - can't remember what it's called) to prove that the dog has been registered, undergone the behavioural assessments etc and the owner the "training" course, none of which a UK owner would have without jumping through the hoops in France. And to do that in France they need to have the dog with them. But the dog's not meant to be in France without papers. Do you see what I mean? It's goes round in blooming circles.
I would have thought if they have the pet passport, keep the dog on-leash and muzzled EVERY time they're out in public they may be okay because no-one would have reason to question them. If they have a thoroughly lovable dog that bears a faint resemblance to an American Staff for example thoroughly enjoying itself racing up and down the beach they could fall foul of the law.