Interrail adds 2€ fee per person per train so it quickly adds up! Optional reservations (in Germany or elsewhere) are also more expensive.
Best to go through the companies when possible. Rail Europe works well for TGVs and cross-border services to Germany.
DB costs 4.90€ per journey and there's a seat map. ÖBB is 3€ per train.
Follow the guide here: https://www.seat61.com/interrail-and-eurail-reservations.htm
Note that part of the Rhine railway is closed for 3 weeks in August. High-speed trains from Paris are rerouted via Saarbrücken and skip Strasbourg. Book well in advance in any case.
As a side note: SNCF has an unofficial offer where they give free TGV reservations to Interrail travellers from France. Only applicable on domestic journeys and you must go to a counter (billet parcours d'approche).