Is it only your date that isn't flexible, or the time as well?

With it being Friday before New Year's Eve I suspect that trains will be quite busy in the afternoon/evening with people travelling for the week-end... but on the other hand it may not be as busy as normal Fridays because many people will have been off work for the whole week. As long as your times are flexible you should probably find something.

The one and only time I travelled on the Thalys I bought my ticket 20 minutes before departure, and there were plenty of seats.