Unfortunately there is a passholder quota on Eurostar services. This is a company decision so they can make more money… You can’t board a Eurostar train without reservations. Otherwise expect a big fine (it’s like travelling without a valid ticket).
Fortunately there are loads of options to go to Paris, only with a few easy changes ! I’ll have a look and update this post. Are you alone and do you have a 1st or 2nd class pass ? Updating...
Option 1 (possible to leave earlier or later for 20€ too; 15:12 - 16:15 TGV at 10€) :
- IC Rotterdam Centraal - Antwerpen-Berchem 09:11 - 10:22
- IC Antwerpen-Berchem - Kortrijk 10:43 - 12:02
- IC Kortrijk - Lille-Flandres 12:13 - 12:51 (often it’s the same train all the way from Antwerp)
- TGV Lille-Flandres - Paris-Nord 13:39 - 14:42 20€ 2nd class or 19€ 1st class (incl. upgrade)
Option 2 (leaving an hour later is cutting it a bit tight) :
- IC Rotterdam Centraal - Antwerpen-Berchem 07:11 - 08:22
- IC Antwerpen-Berchem - Kortrijk 08:43 - 10:02
- IC Kortrijk - Lille-Flandres 10:13 - 10:51
- break + short walk
- TGV Lille-Europe - Paris-Nord 12:05 - 13:24 10€ 2nd class
Also possible to leave earlier and stop en-route (hourly service). Book the TGV on eurail.com or here (especially if you want the upgrade) : https://travel.b-europe.com/Eurail-GE/en/booking-tgv#TravelWish
Option 3 :
- Eurostar Rotterdam Centraal - Marne-la-Vallée-Chessy TGV (Disneyland) 07:58 - 10:48 32€ seat reservation
- RER A to the city center about 5€ for a ticket (not included)
Option 4 (long but fully free) :
- IC Rotterdam Centraal - Bruxelles-Midi 08:11 - 10:16
- IC Bruxelles-Midi - Charleroi-Central 11:07 - 11:57
- R Charleoi-Central - Maubeuge 12:24 - 13:20
- TER Maubeuge - Paris-Nord 14:42 - 16:42
Do not hesitate for questions !