Trains between Paris and Amsterdam

Yes, although I don't know the details on Paris to Brussels that well. From Brussels to Amsterdam, there's a regular ICE train that leaves about every hour. Over the PA system, you'll hear it referred to as "the international train to Amsterdam/Brussels". No reservations are necessary or possible. I don't know if there are any extra fees for passholders.

There are definitely regular non-Thalys expresses between Brussels and Amsterdam that are cheaper and only a bit slower. (I think Tom mis-typed: these are branded "IC" or "Inter-City", not "ICE" which is the German ultra-high-speed trains.) But there isn't an express alternative between Paris and Brussels, and I have a nasty feeling that the slower trains are deliberately designed not to provide a usable alternative. You may have to go to Lille and make a detour via Ghent to get to Brussels.

"They are really expensive even with a pass" Thalys between Amsterdam and Paris isn't expensive at all. If you book early enough you can get restricted fares for just 35 euros. If you take the regular inter-city train via Brussels and Lille it will cost over 80 euros and take longer. Stick with the high-speed train. http://www.thalys.com

go thalys it is worth it. faster, some amenities. you are on vacation. get there as fast as you can. have fun, be safe.