Eurostar have 17 Class 374 sets, which just about stretches to do:
-Hourly Paris services (about 7 sets)
-Hourly Brussels services (about 6 sets), plus 1 "train in steam" beyond Brussels to Amsterdam
-1 set for Disneyland
That leaves one set for 'other' stuff - either extra Paris services or south of France services, plus one maintenance space.
You could of course have a less frequent Brussels service to free up sets for other things.
So Eurostar could stretch a credible service together with just 374s, but not much room for expansion.