I plan to buy a Eurail pass that enables me to travel from France to Italy. I plan to buy the France-Italy Rail Pass, but I don't know whether I would need to buy an extra pass because from my research, the train will have to stop at Geneva, which is located in Switzerland.
Do I have to buy an extra pass for this purpose?
Edit: As I research further this train comes to my mind (TGV 9249). I think this is really what I really need; am I right?
If you want to travel by train from Lyon to Milano, it is not necessary to pass through Geneva or any other part of Switzerland. The most straightforward option is to take a regional train (TER) from Lyon's Part-Dieu station to Chambéry and then a TGV to Milano. This train is going to Milano via the Maurienne valley and Torino. At the moment there are two or three TGV trains per day linking Paris to Milano via Chambéry and Torino.
The TGV 9249 seems to fit your needs, as it does not cross Switzerland. On the 12th of May, you can leave Lyon Part-Dieu at 14h40 by the regional train bound to Bourg-Saint-Maurice. Ar 16h00 you will arrive at Chambéry-Challes-les-Eaux, where you will have to get out and wait for the TGV 9249 to Milano, leaving from there at 17h43.