Oui, c'est possible. 

But according to the Outbound/Inbound rule, you can only use a maximum of two travel days in your country of residence, France. 

If you only will make the trip from Italy to France and back it might be cheaper to buy ordinary tickets. In addition to the global pass, many trains in France and Italy require a seat reservation.

It is possible to travel without reservation in France and Italy on many regional trains. You need to look at the route you plan to travel.

Thank you so much. So if I understand it well I can make Italie-France and France-Italie the day after, but I can’t back in France again. Is it correct? I think it would be interesting for me anyway during the summer because I will do other travels in Italy and that I will be with my 8 years old daughter, that will pay only seat reservation. 

Yes, that is correct. You can use 2 travel days in you home country so when going back to France again you need a ticket from the French border.

You need child pass, which is free of charge, for your daughter and then you pay the seat reservations for her.

I hope that you will have a nice trip.

There is a very high supplmt with any pass-in fact the highest there is for direct TGV Paris-Milano: around/over 50€. Check if that is worthwhile with also cost of passday

TrenItalia now also has trains on its own, NOT taking passes, so there is even competition to this state owned national society of yours-they may offer lower prices, but it all depends on where you start/go to.