For the Paris to Nice trip, and maybe also Nice to Rome you can call SNCF (the French Railway)
https://www.sncf.com/en/customer-service/contact-us/telephone
Press #85 for English, no booking fees, reservations are sent via e-mail.
The trips within Italy can be booked at ÖBB (the Austrian Railway) if it not is a night train.
Here is guide on how to make reservations:
From NI onward to IT there is simply as for now NO direct treni: its local=UNreserved till Ventimiglia-or even further, then TrenItlaia-choose. 1st cl in local treni there is just the same as 2nd-maybe anohter color of seats-but mostly not respected at all.