Amsterdam to Paris with Stopever in France

Lille or Amiens.
Lille is on the high-speed Eurostar line from Brussels to London. As far as I can see Amiens is another 1,5 hrs with a regular TER train. (The train planners of the Deutsche Bahn and the SNCF route you via Paris, which in your case would be somewhat ridiculous.)

While Eurostar trains stiop in Lille, Thalys trains stop in Rotterdam, Antwerp, and Brussels. Assuming you can afford the Thalys fares (non-changeable, non-refundable) and assuming they offer a stopover option, I'd strongly recommend Antwerp. (I liked Lille.)

I found it hard to make the Netherlnds, Belgium, or German rail websites show me non-Thalys options. But you could enter (for example, a place I'd like to visit ...) Lens, France and see what comes up. Note that train prices tend to go up as departure date approaches. Some faster but non-Thalys services can require seat reservations.

"I found it hard to make the Netherlnds, Belgium, or German rail websites show me non-Thalys options."

It's not too diffucult on www.bahn.com.

Either add a stopover(default setting is 0 minutes) at a station where Thalys doesn't stop or make a basic search and filter out high-speed trains by clicking on change, than change other data, than conections - more means of transport, than take the ICE option out by "de-clicking" the first box.

Or simply do separate searches: Amsterdam - Antwerpen, Antwerpen - Lille, Lille - Amiens, Amiens - Paris.

I found the international section of NS, the Dutch railways, also offering non-Thalys options with intercity services from Amsterdam to Antwerpen/Brussel and from there to Lille.

The fast (3h 20m), direct Thalys trains between Amsterdam and Paris don't make any other stops in France; only the Dutch and Belgian stops that Tim described. Therefore, whatever destination you choose is a bit of detour off the "main" train line and will add some travel time, though that can certainly be worthwhile to add a destination that you want to visit.

Another tactic would be to add the day to Paris, where we can almost always spend more time, and make a daytrip out from there if you wish. Some common daytrip destinations, such as Chartres, are relatively short and cheap train tickets to buy on the spot. Others, such as Reims, have been made "closer" by the advent of more expensive high-speed trains that you might want to book ahead.

Thank you all for the great suggestions