Seat61 will explain the difficulties of Eurail (and other) passes. The simplest is that TGV trains, among others, require a seat reservation for a time and day. It has to be purchased separately from the pass, at extra cost, and there are rumours that only a quota of seats qualify.
RailEurope is an agency which, although apparently connected to the SNCF French train operator, is not the best source of information. You can go directly to the SNCF site to see (and buy) TGVs and other services:
Tickets bought here include seat reservation. Some US customers have reported rejection of their credit cards but my Canadian cards have always gone through.
The site shows a night train leaving at about 9:30 p.m. It requires two transfers to get to Genoa and only the first is a true sleeper service. Time elapsed: more than 15 hours. I love trains, but not that much, especially when all you can see out the window is darkness. By air, 90 minutes. Add in three hours for all the complications of getting to and from airports and security, and you are still far ahead and better rested. Plus richer: Bought far ahead, Air France among others will charge you about $100, a good deal less than the train fare.
(PS: I'm sorry, but the North American assumption that train passes are worth it is outdated. It is always wise to do the point-to-point pricing first when planning, and go to the sources rather than an agency. Just ask Seat61.)