You don't see available if you not are logged in. Pass holder seats on the Eurostar during the holidays have been sold out for weeks on most departures.

There is a limited number of pass holder seats on the Eurostar and on popular departures and during high season those sell out weeks, and sometimes months in advance.

The best place to see the availability of passholder seats and make reservations on the Eurostar is 

https://www.b-europe.com/EN/Booking/Pass#TravelWish

Press "later trains" and eventually you will find the next available connection. 

If you have a mobile pass you need to generate a Pass Cover Number in order to make the reservation at b-europe. You do that here in the PCN generator:

https://community.eurail.com/news-and-announcements-39/pass-cover-number-generator-is-live-5653

This information is given on the Eurail website.

You'lld better look for alternatives if you really want to travel on that date.

The first available departure is on January 2nd. It's a very plane like system. Luckily it's one of the only trains that is so annoying to get places on. 

You can buy ordinary Eurostar tickets, but so short of departure they will be pricey. (Book directly at the Eurostar website) 

There are suite some coaches to Paris too, usually taking the ferry. The crossing is quite nice, with a good view on the cliffs and plenty of amenities on the ship. This is probably the most cost-effective solution at this moment. But not included in the pass. 

Reservations on Eurostar are 30 EUR for a seat.