2 Answers

Looks like there is only one train and one route and the train is pricey. Now mind you, I'm just going by this webpage I found. There may be trains that they did not mention:  

The night train from Paris to northern Italy is called Artesia. It takes about 14 and a half hours to get from Paris to Rome. It leaves Paris from the Gare de Bercy Train Station. You must reserve your space on the Artesia and pay a supplimental fee. If you have a France-Italy rail pass you will pay less.

Many people like this option, although even with a rail pass it could be more expensive than a budget airline. Passengers cite the scenery in southern France, eating a meal while that scenery is passing by, and having space for the kids to play.

All passengers on the Artesia sleeper trains from Paris to Italy must reserve a sleeping berth in either a sleeping-car or more economical couchette car (4 or 6 bunk-style beds.) You cannot just book a seat on these trains, although the beds convert to a seat for the morning.

For more information and ticketing on Artesia, see the Rail Europe FAQ on Premier Trains.

For a regular rail pass that covers France and Italy: France-Italy Rail Pass (Buy Direct) 

Information source: http://goeurope.about.com/od/transportation/a/paris_to_rome.htm

my wife and i went from Paris to Zurich to Rome,,,different train company's mean you will change trains,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,