SNCF doesn't offer reservations on their website because "too many people misused the option".
Cross-border TGV/ICEs are only available online on eurail.com : 17€ seat reservation in 2nd class + 2€ fee per person per train.
You can call SNCF but they don't accept all credit cards (annoying for a big company). No fee but you pay the call : https://www.sncf-voyageurs.com/en/customer-service/contact-us/telephone/
Btw it is much cheaper (free) to take the Offenburg - Appenweier - Strasbourg regional train across the Rhine. You've also got a lot more flexibility :)
It depends on which route you will take.
If you take ICE to Basel, then TER, there is no compulsory reservation. You can reserve the ICE on the DB website.
If you take the ICE or TGV to Strasbourg, then TER, there is a compulsory reservation on the ICE or TGV - because it’s international. You should be able to buy this on the Eurail reservations service for €18.
https://www.interrail.eu/en/book-reservations#/