I know nothing about this specific painting but the fact that it was painted by an Italian artist in Italy is a red herring.

As far as I understand the law allows any significant art piece in France to be deemed a National Treasure. Think of it more as an important asset for the country rather than something that was made in France or by a French person.

In French the definition is that it is important to the national "patrimoine", which is the same word used to refer to someone's assets/estate.