On the Italian side it won't be a problem. When women get married they do not take their husband's name. The children do. So it is the norm for mothers and children to have different last names. I don't think you'll have a problem in France because I think there it is illegal for a woman to take her husband's surname. In Italy its not illegal, there's just no legal mechanism to do it. The wife is given an option to have a hyphenated surname combining hers with her husband's, but most don't. The children always get the father's last name, so the expectation is that the mother and childrens' passports will have different surnames.