If you only are going to Italy it might be cheaper to pay for the ticket from Paris to the Italian border and then buy some type of pass for Italy.

There are others in the community who know more about Italian trains than me.

If you want to travel in more countries than Italy, then you should consider a global pass. In a global pass you can travel on 2 days, outbound and inbound, in your own country. Thus the trip from Paris to the Italian border would be included except for a possible seat reservation fee.

if you have a country pass, the French trains are NOT included. 
 

if you have a global pass, the French trains are included, but you will need reservations on the routes between Paris and Rome. And it can be quite difficult, as the number of available seats is limited on French TGV trains.

Alternatively, you can use regional trains on parts of the journey - they do not require any reservations. But it takes longer time.

There is no direct train Paris - Rome. There are direct trains from Paris to Milan: TGV and Frecciarossa. Only the TGV is included. From Milan to Rome, you can take a Frecciarossa, which is included in that case. Reservation fees can be found here.