It's easy to prove this paradox nonetheless. Just check for instance the way we inflect the verb "to be" at present indicative.
Latin -> Suis, Es, Est, Sumus, Estis, Sunt
French -> Suis, Es, Est, Sommes, Êtes, Sont
Italian -> Sono, Sei, è, Siamo, Siete, Sono
But the truth is that in written form, Italian and French are almost mutually intelligible. Italian and French are closer than, say, Italian and Spanish (Even if Catalan is the closest relative of modern French). It's like a Swede speaking to a Norwegian.
As a French, the trick I use to understand Italian is to deliberately forget the proper "noble" Latin root that you can still notice in most French words, and focus more on the way it sounds (or rather, the way it should have sounded).