You should go from Fiumicino to Rome Termini station, and from Termini there are trains which go through Arezzo - so you don't need to go to Florence.
To get from Rome Fiumicino to Arezzo, Tuscany, I would suggest travelling into the center of Rome and then catching a train directly to Arezzo.
Travelling from Fiumicino to Arezzo
Unfortunately, there is no direct train from Fiumicino to Arezzo, so your journey will have to be completed in two parts:
Getting from Fiumicino … Read more