Never trust the planners of the rail planner ap, nor the Interrail website. Base your information on the transport companies itself (Eurostar in this case) or use a reliable planner that encompasses most of Europe. Deutsche Bahn has up to date information for most of Europe.
Book your Eurostar seats asap. They can sell out. Sometimes weeks in advance. Only a limited number of pass holders are admitted on each train. This can be done via the reservation section on the Eurail/Interrail website. Or follow the steps via this guide, alternatively.
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
There are no trains with pass holder seats between London and Paris on the 10th, 11th or 12th of February. There is availability on 13th of February. I checked 2nd class availability.
In 1st class there are pass holder seats available on the 11th and 12th from London to Paris.
If you really need to travel that day I'd consider Flixbus or similar (unfortunately...).
As @AnnaB said there are no passholder fares at all and almost no regular tickets left, at more than 200€. Either you could consider travelling another day or a bus…
There are also ferries between the UK and France, although they take much longer. Please have at look at seat61.com
Edit : Flixbus would cost 75€
There is (limited) availability on Thursday 9th of February to Lille, on the last train (dep 19:34 London, arrival at 22h). From Lille you have plenty trains (domestic French TGV's) to Paris, although not that late. You will need to stay overnight in Lille then. Saturday 11th only limited first class availability on one train (to Lille).