Not directly a channel tunnel service, but GoVolta (a Dutch open access Operator) has applied to operate services from Amsterdam to Brussels / Paris including high speed services.
It would mean Eurostar Red (the ex Thayls services) have low cost competition on Paris-Amsterdam corridor and might affect how its fleet get deployed
GoVolta seem to do rail & hotel packages, so to some extent seem to operate like some European low cost airlines with their city break packages
There is a map on GoVolta website
Amsterdam <> Berlin & Paris · Book now your train city trip.
govolta.nl