i live here in florence, i would recommend you to go only from florence to rome, having only 3 days to spend, it wouldnt be worht seeing florence or rome to paris. i once took a train from florence to paris, and it was a long long long trip, and it cost me about 150 euros round trip. with in three days only you would be wasting your time on an overnight train ride than enjoying your trip. IF you can find a cheap airline ticket from florence to paris or from rome to paris, then its ok i suppose, but risky since your tight on schedule.
so from florence to rome, or rome to florence you can choose any type of train, there is the direct, intercity, and eurostar. the intercity is the cheapest although its the slowest since it stops in almost every single stop on the way. if you take the direct, it stops only in the main stops. the eurostar, is the fastest and yet most expensive. however from florence to rome in the intercity its about 20 euros, the eurostar about 30. so its only about 10 euros difference. however pay attention because the eurostar has limited seats and i recommend you to make reservations before hand NOT on the day of your departure. the intercity or hte direct doesnt have a limit of passengers so that one you can buy on the day you leave.
at the train stations there are these big yellow machines from where you can buy and purchase the tickets without having to wait in line in the ticket booths. the machines come in any language so they are easy to follow and some of them allow credit card or cash, check before you begin using it. remember to VALIDATE your ticket before taking the train or else you get a 30 euro 'multa' for not validating it. you can validate the tickets in any ones of those small rectangular yellow ticket machines by every train.
ok, hope the info helps.