If you are willing to spend the extortionate charges incurred for renting a car in France and dropping it off in Italy, the 285 mile car journey will take you more than five hours, plus any time you spend at stops on the way, so maybe six hours.
The fastest train journeys take around 7.5 hours, though to leave around 12 it will take around 8.5 hours. And these trains take a much longer route, via Milan. http://www.tgv-europe.com/ will give you a through booking from Nice, though for some reason not from Antibes even though most of the trains from Nice it uses also call at Antibes 30 minutes earlier …ter-sncf.com/Images/Paca/Tridion/FH04-Mande… And it may be advisable to leave Nice/Antibes 30 minutes earlier than suggested by the website to ensure the connection at Ventimiglia if the French train arrives late.
Trains by the shorter route via Pisa are usually slower and with more changes, but can be significantly cheaper. For this route, see http://trenitalia.it/homepage_en.html for Ventimiglia-Florence, and buy a local ticket for €9.50 for Antibes-Ventimiglia (the tickets are OK for any train until validation as these trains have no reserved seats).
The final route is to take a cheap flight by easyJet or Blu-express from Nice to Rome, then train to Florence (around 2.5 hours from Fiumicino Airport train station including a change in Rome). In theory you might manage the journey in around six hours this way if flight times and connections are good, but this needs checking out properly, and I think easyJet flights usually arrive too late in Rome to get to Florence the same night.