Fine, they all do indeed sometimes show different availability. All part of the Interrail mystery process.
But agreed that booking to Karsruhe would be just fine (subject to right kind of reservation, see below).
GBP18 sounds like EUR20, which is the non capacity constrained reservation charge for TGV/ICEs in France. Strasbourg-Paris by ICE seems to be charged at the same (at least for Interail purposes) as TGVs are.
NB getting a reservation-only ticket via DB/DB Navigator is very much not recommended. The reservation must state 'Interrail/Eurail' to be valid, those from DB are those with completely flexible tickets seeking a seat reservation only.
More formally, note that DB/SNCF have a formal (and EU Commission-approved) agreement for crossborder TGV/ICE trains, covering marketing, capacity and pricing. They are not at all 'competitors' in the way that GB TOCs are.....