You will need reservations for most of these trains. If you buy a ticket (in advance or on they day of travel, online or at the station) any required reservations are included. If you use a rail pass, you have to buy a separate reservation.
For France, the number of reservations available to rail pass holders is limited for each train. So, even if there's space on the train, once the rail pass holder reservations are gone you can't use your pass. You can then either buy a full ticket (no longer cheap since it's close to travel) or take a different train that does still have pass holder reservations available.
For this reason, even Rick Steves recommends getting all of your required France reservations at the time you buy your pass - negating one of the main potential advantages of a pass, spontaneity.
Also, French train tickets can be quite cheap if bought in advance, as long as you can live with non-refundable and non-exchangeable tickets (or tickets that severely limit those actions). Since it sounds like you already know when you're traveling where, this shouldn't be a problem. Full fares on some trains in France can be quite high. On the other hand, if you buy French rail tickets right when they go on sale, you can often get first class for just a few euros more than second class!
For Italy, reservations are not quantity-limited for rail pass holders. Here, the problem is that regular fares are low, and advance purchase fares are even lower. So, a pass is a waste of money.
If you want to learn more about the issues of using a pass vs last minute tickets vs advance purchase tickets, read this great summary from rail guru The Man In Seat 61: https://seat61.com/Railpass-and-Eurail-pass-guide.htm#railpass-or-point-to-point-tickets
To find schedules, including which trains have mandatory reservations, use the Bahn (German Rail) website http://reiseauskunft.bahn.de/bin/query.exe/en, following Rick's tutorial: http://www.ricksteves.com/travel-tips/transportation/trains/online-schedules
To find out where to buy tickets, go back to The Man In Seat 61: https://seat61.com/Europe-train-tickets.htm