For TGV within France https://travel.b-europe.com/eurail-ge/en/booking-tgv?#TravelWish

There are various ways to make reservations (and check availability) for French trains. 

You can call  b-europe and make the reservation. 

The phone call is rather expensive.

https://www.b-europe.com/EN/Contact/Contact-Centre

Another way to make reservations for French trains is to call SNCF. 

https://www.sncf.com/en/customer-service/contact-us/telephone

 Press #85 for English, no booking fees, reservations are sent via e-mail. Not all credit cards are accepted.

For domestic French reservations, you can also call NS. Also no booking fees and they do accept VISA. Remember the country code (+31)

This in fact only relates to TGV-and the 3-4 overnite trains:

there is a quota for passholders-then its 10€ extra, this may be very small or 0

IF this is taken-then the price goes to 20€ (more as very short trips at full fare) and that is as long as there are seats-which you can easily check by making a dummy booking normally.

This is for domestic=inland, its different for overtheborder, but from DE you can easily use local trains to hop over.

On most main lines you can always go via the local TER trains-via what they call the ´classic lines´-then you will note how much faster these TGV travel have made-and FR is quite big-

@mcadv  Many thank for the tip. Actually, this is also what I finally discovered, that it is easier to find reservations in France instead of overt-the-border. Now, I found a train from Strasbourg to Paris.