What route are you trying to book? Most routes can be booked without Pass Cover Number.
The best way to make reservations for French trains is to call 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
To get your Pass Cover Number, if you still will need it, you need to contact Customer Support through this form and ask for the Pass Cover Number.
https://eurail.zendesk.com/hc/en-001/requests/new
Customer Support is currently overloaded with requests so you will probably have to be patient to get help. Please let Customer Support know what date your travel will start so that they can prioritise your request correctly.
Hi AnnaB,
It is a TGV train between Paris and Bordeaux is it also possible to make a réservation for that by falling SNCF?
Hi AnnaB,
It is a TGV train between Paris and Bordeaux is it also possible to make a réservation for that by falling SNCF?
Yes, that can be booked by SNCF.