@Angelo 

Thanks for tagging Anna!

You have to compare the ticket prices of the trains with the price of the Eurail Global Pass + Reservation costs. How many days you need for the Eurail Pass depends on how many travel days you need. There is a Eurail Pass for 15 days continuous for 359 US$(adult), this means you can use trains every day. Or one of the x days in 1 or 2 months. 

Reservation costs: 

France: Paris-Nice 10€ or 20€, From Nice to Ventimiglia (border to Italy) you take a TER train (no reservation needed and possible). Reservations bookable online with mobile pass only via eurail.com, but there are some problems with the 20€ reservations. Maybe you have to ask custumer service to get a paper pass cover number to be able to buy the reservation online via B-Europe or you can call SNCF call center (press #85 for english) or SNCB call center. 

In Italy for high speed trains like Frecciarossa, Frecciargento, Frecciabianca and Eurocity within Italy you pay 10€/train. For Intercity (IC) you pay 3€ per seat. In local trains like Regionale or Regionale Veloce (express) you only hop on the train and add the trip on your pass before boarding. Reservations can be booked online via Austrian railways ÖBB via tickets.oebb.at choose your trip and click on one way ticket and at adult add as discount Interrail/Eurail Global Pass. 

For the Eurocity Italy-Switzerland it cost 11€ in 2nd class the reservation. Bookable like italian trains via ÖBB. 

For the TGV Geneve-Paris you can book it online via Eurail.com or at train stations in France or Switzerland. 

Use 7 day pass and buy single LSp→ Fir (around 10€). That makes the 8 trips.

There is also an overnite train with seats and cochette=lie down bunks P→ Nice. Daily.