Eurostar can sell out weeks in advance unfortunately. One of the worst trains of Europe for that. And the King's coronation doesn't help…
What is your exact travel date so I can have a look ?
There is a work-around by taking the Eurostar to Lille (30€) and then a TGV to Paris (10€). Doesn't take much more time and there's often more seats available.
There is a limited number of pass holder seats on the Eurostar between London and mainland Europe. 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
If you don't get any result, 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