There are multiple ways to book reservations. In the app itself, you can't book reservations but it can forward you to some of the websites where you can, including Eurail's own website. Here is an overview of the most important websites to book reservations (with instructions) and an overview per country.

For more detailed advice on booking reservations, please post for each train you'd like to book: origin, destination, date, departure time.

August 30

Paris Est to Strasbourg tgv2407

07:58-09:58

September 1

strasbourg to Dijon ville tgv9877

09:05-11:16

september 3

dijon ville to Lyon part-Dieu tgv2203

09:23-10:58

september 5

lyon part-Dieu to marseille st-charles tgv5102

09:06-10-46

september 9

marseille st-Charles to Nice ville ter17479

09:57-12:41

Allo de France maintenant ici.

In FRance TER=local trains canNOT be even booked. Same as the Toronto GO-ONtairo trains.

If youre willing to use alternative times-and a little bit slower, you can also do Di→ Ly and Ly→ Mrs by local TER train-they run regularly at least ev 2 hrs. all day and make more stops en-route.

Str→ Di also, but that will take much longer and have more changes. The planner app can also set to NO REServations to have a look at how it looks like then.
you do not really need to fret, except as a general warning for 31/8 and 1/9-the FRench call this ´les grands departs´ =when the major summer holds finish-and they always seem to like it have all at the very same time to enjoy the big overcrowding that then happens. But that is TO Paris then and not really for the bieznezmenny that mostly use 1st. 1st also gives you access to rail-lounges in major stops (most of those)-but they do not offer very much except a tiny cup of cf or some OJ and a lot of French journals=newspprs.

You have the pass already but seeing if these are the only intended trips then its bad value-if you are so convinced now already that it must be that day and that time-simply booking advance tickets might have been at total lower cost.

The train on 9 September is a regional train (TER) for which there are no reservations.

The other reservations can all be done via Eurail, with a booking fee of 2€ per person and train, on top of the 10€ reservation (current price per person; can go up to 20€). Alternatively, you can call SNCF (press #85 for English) to book without any booking fees but the call will of course not be free.

For the journey on 3 September there are also reservation-free options leaving at 8:40 and 10:41 that only take half an hour longer than the TGV.

For the other journeys there are also reservation-free options but the additional time needed is much more. Although on 30 August, the direct reservation-free TER Paris Est 7:36 - Strasbourg 12:34 could still be interesting.