It is surely a Ouigo train (low-cost subsidiary of SNCF). On these trains the pass is not valid. You need to buy a regular ticket on sncf-connect.com, they're quite cheap especially so long in advance
Otherwise take a TER train to Marseille and from there a regular TGV (10-20€ seat reservation). It looks like that you can arrive in Paris at 12:22 by leaving Antibes at 05:47. You can take the Eurostar at 14:43 (13:13 would be a bit tight as you need to change stations + pass border control).
Or direct TGV Antibes - Paris 08:14 - 13:50 and a later Eurostar
Many thanks for the info! That’s very helpful.