From the seat61 page you linked to:
prices vary like air fares so you'll find fares from around €27 if you book in advance
As LostInAmerica has shown, it looks like the cheapest tickets have either already sold out, or weren't event available. Thalys tickets generally go on sale 90 days in advance, and it looks like the very cheapest ones have already been snapped up, sorry
Cheap Thalys tickets are only valid on one train, and that train only. On the other hand, the regular trains are only €39, ticket valid on any train, you can buy on the day, and it isn't that much slower. Maybe just get one of those?