You may try here

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

or try calling SNCFs hotline. You would safe the booking fee that way.. GL

You can book by phone at SNCF. No need of Pass Cover Number. 

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

 Press #85 for English, no booking fees, reservations are sent via e-mail.

Thanks, AnnaB. 

But on this link only accept passes on paper. I have a digital one. Where is my pass cover number?. 

Thank you, 

You won’t need it. They will only ask you name, e-mail and maybe birthdate I don’t remember. Not cover number. 

Thanks!

I will try this option.

Explan: the FRench call this ´les jours de grands departs=end of main hols.

The normal quota for TGV-pass seats (small, then it 10€) is sold out-or I suspect 0 on such days. The then 20€ seats canNOT be offered as such in the app-that is some quirk that was pointed a few 100 times. Hence need to call.

But last yr I could -without much choice-even find seats for 20 on a TGV from Bordeaux to Paris on such a day a day before.