I would really hate having to rush through all of Italy, let alone France, in less than two weeks.
Let's say you'd effectively have 12 days, excluding the trip to and from Rome.
You'll need at the very least four days for Rome itself, which leaves eight.
A few day trips from Rome would be in order, let's say one to Ostia, one to Hadrian's Villa and Praeneste and one to Cerveteri and Tarquinia. Five days left. Pompeii is a must, and you might as well rebase to Naples. So that's one day for Pompeii, one day for Herculaneum and nearby sites (Boscoreale, Oplontis, Stabiae), one day for Naples itself, one day for the campi Flegrei (Cumae, Baia, Pozzuoli) and then there's just a single day left. An agonizing choice between many of the great sites that still remain in the proximity of Rome and Naples: Capua, Benevento, Capri, Nemi, Albano Laziale, Terracina, Gaeta, Veii etc etc. That's 12 days of top tier Roman sites, all within an hour's driving from Rome and Naples. What's the point in crossing half of Europe, too essentially see less because you lose so much time in transit and changing hotels every day? Just my 2 cents.