Next month we are doing a trip that combines Tuscany with Provence. We have two options and hoping someone out there with experience can chime in.
TRAIN: Regional to Pisa, then Pisa to Genova, then Genova to Ventimiglia. Once there, a French train from Ventimiglia to Nice. This plan forces us to be on the first train at 7:00AM and we don't get to Nice until 3:16. There is a way to get there an hour earlier but there would only be at time 14 minutes between train transfers.
PLANE: Train from Florence to Rome, then take the Leonardo Express to the airport, then EasyJet to Nice. With this plan you start around 8:30 in the morning and land at 1:15 or so.
BTW, originally we were going to spend a few days in Rome (we've been there) but had to shave off a few days of the trip for a family commitment. So yes, it would be a GREAT idea to just spend time in Rome but we had to nix that to make all the days fit.