Have to say, Pierre is the most "Italian" of the Casiraghis to me. It seems like, living in Italy and taking Italian studies, he feels a real connection to his father's heritage. I'm not saying that Andrea and Charlotte don't, it's just Pierre seems the most "proactive" about it.
About what language they speak, I know that they speak English with an accent (Andrea has quite a pronounced one), I'm just saying that I've heard more than once that Pierre speaks a blend of English and Italian. The Grimalidis, Casiraghis and Hanovers speak English far more than I would expect of a sovereign family of a French speaking country. Alex can speak German (we heard that on the Fête Nationale broadcast a few years ago, when she talked to the cameraman in German), Caroline can speak German and Ernst can speak French. But they talk to each other in English, because it is a language they are both efficiently fluent in. And it would seem that the Casiraghis and their friends speak English amongst themselves as well. I think there's a part of one of the videos about the Rose Ball where you can hear their friends talking at the table in English. Nobody ever said that the Casiraghis don't speak French. On the contrary, they probably speak it a lot. After all, as you pointed out, they do come from a country where French is the official language. But there's nothing wrong with blending languages into a dialect of your own (kind of like Spanglish - but not the American version. "Trucko"? Seriously?
). It doesn't mean any language is valued less or anything. Particularly when, in other languages, you can express in one word a sentiment that would take a whole sentence to explain in English. So I think that the family, knowing and speaking as many languages as they do (they all speak French, English, German and Spanish - Caroline speaks Italian and Albert speaks Portuguese, I'm not sure how many of them are capable of speaking Monegasque - Stephanie's children probably would given that they were raised largely in Monaco where it's part of the curriculum) they just talk in whatever suits best, knowing that everyone will understand. I happen to think that a person who can mix languages comes across as smart and well educated and, dare I say it, a little exotic.
I hoping you mean Vincent Lindon too. We certainly missed something if the trio grew up with Junot for a father figure.