With a PassCoverNumber (Paperpass in case of Mobile pass you have to request for such one)  on the website of B-europe https://travel.b-europe.com/Eurail-GE/en/booking-tgv#Outbound

Thank you. They are not answering the phone number listed on the website. Is there another way to contact them to request this “Pass cover number?”

Domestic TGVs in France can also be booked via NS. No pass cover number needed, no booking fee. Visa and Mastercard are also accepted.

You can also call  b-europe and make the reservation. No need of Pass Cover Number.

The phone call is rather expensive.

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

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.

Customer Support if Interrail have no phone number.

You can contact them via Twitter, Facebook or this service form https://eurail.zendesk.com/hc/en-001/requests/new

They were nice! I am still trying - but now need to upgrade to 1st class eurail to get a seat… At least they take multiple forms of credit. Still unresolved, but trying. Thankyou!!

For domestic TGVs in France, there's a specific pass fare that allows 2nd class pass holders to use 1st class. It's a bit more expensive of course but usually quite OK.

Do you know how to ask for that specific pass fare? what is the name?

Belgian railways call it "Pass Eurail Upgrade”.

Travel Conditions: “Passholder fare only valid if used in conjunction with a 2nd class Eurail Pass covering France and who wants to travel in 1st class. The journey travel date must be within the validity period of the pass. Fare with limited availability.”

Thanks @rvdborgt  for helping me to find the best solution. You are a hero for directing me to NS  - it really worked ! A kind, intelligent, skilled customer service professional managed to book my seats and talk me through what was happening, How ridiculous that the Dutch are fixing the French rail challenges! The NS phone line is open 24/7 and the agent had perfect English and understood my challenges 100% He explained that there are limited seats for Eurail pass holders. Also, the system won’t book a seat for a long distance voyage, like Paris to Montpellier, if any single segment does not have a seat available. So he went at it segment by segment to see where the block was. I paid a service fee -but it was well worth it. In the end, I kept my second class eurail pass and didn’t get exactly the train I wanted, but I was able to reserve a seat, pay with a VISA (instead of SNCF workaround which was “borrow your friend’s AMEX) and go to and from the places I want. I also understood that three weeks before travel, especially during the French school holidays is considered “late.” If I had known eurail SEAT booking would be so complex with Eurail, I would have opted for buying straight tickets - no pass. HUGE GRATITUDE to this c community when Eurail, SNCF, Rail Europe did not have a system to help me.  

Wow, you really had an experienced member of staff. 

Although they shouldn't have charged, since they don't do that anymore for tickets and reservations that cannot be bought via the NS website.

French trains can indeed become fully booked rather fast around holidays. I've seen that multiple times. The long Ascension day weekend is notorious for that. Even 2 months in advance it was already beginning to get difficult to find seats at all.

It's not Eurail, it's the individual railway companies (in this case SNCF "we decide what you have to want”) that make it difficult - both and for passengers and for Eurail (who are not particularly happy with some of the railway companies either but probably won't admit that publicly...).