Have you tried at b-europe?

https://travel.b-europe.com/Eurail-GE/en/booking-tgv#TravelWish

You need a Pass Cover Number if you have a mobile pass. You get the PCN here:

https://community.eurail.com/mobile-pass-62/pass-cover-number-generator-is-live-5653

These are TERs with mandatory reservations, an invention by SNCF Normandie. They can't be booked online, only at the ticket office or ticket machines, anywhere in France (add Interrail as a discount). Price is €1.70. Availability usually isn't a problem even last minute, except for weekend days in summer, when it's best to book a few days in advance.

thank you for your answer! I didn’t know about that website yet.
But - it won’t show me any train on my selected date, even when I try earlier or later departures…?

thank you for your answer!

OK, that helps me keep up my hopes a bit. We arrrive 2 days earlier in Paris so we could try to book the reservation then on a machine. It’s a monday mid august though….

That should be OK. If not, let us know here and we'll figure out alternatives.

Now that we’re back from our trip, I can absolutely confirm what you said. Booking a reservation is possible short term via the ticket machines! Thanks again for your answer!

(we had some problems with the machines, though and due to our misunderstanding we paid for the second train after Caen the full price because we couldn’t add the interrail discount for our 11 year old child at the ticket machine. We were confused, e had little time but later realized, that there should have been another way.
That just saying for other travelers: take your time with the machine (and it MAY NEED TIME ) or take more time and wait at the ticket office, so you can ask questions and get helped. )

I always like to read a short and nice feedback on this forum on how things went eventually.

It helps finetune our advices here

I’ve been in Cherbourg recently and even though the app showing reservation mandatory, the ticket clerk in the office told me it is not and also the conductor didn’t ask for any reservation. Could someone of the Interrail team clarify this and correct the information if it is true? Would make things for some people a lot easier if you don’t have to worry about reservations…
Seats reserved are displayed on the train, so it is easy to find non-reserved seats.