Air France are sending emails informing that the flights into Florence airport will be diverted to Pisa airport. It doesn´t look as if they would be transporting people into Florence, but Pisa is very near and there is a train service from Pisa airport into Florence, so you should be OK.

The timetable for the train service : http://www.pisa-airport.com

Kind regards, Covadonga Bilbao/Madrid - Spain