Only 2nd class is fully booked on the morning train at the moment. But you can't book this route on eurail.com for a few days supposedly due to a bug…
Use the options provided by rvdborgt or wait a few days. Please note that SNCF may only accept AmericanExpress.
Any updates on this @Mukhammad @Camilo. ? This is such a popular route and a confusing situation... (as the trains are not sold out but people believe so)
Where does Eurail say that? SNCF removed that possibility about 3 years ago from their website.
Here's a list of known possibilities to book Barcelona-Paris: