Stephen, the primary fast train system between Amsterdam and Paris is the Thalys system. As Tom indicates, they are not kind to Eurail passholders. In fact, to travel on their trains, you will have to pay an extra supplemental fee on top of the cost of your pass. It's one of the highest in the EU. For example, from Amsterdam to Paris, it's an extra 39Euro. I can buy an discounted ticket on the Thalys train for this price. Also, Thalys limits their seats to passholders. If the passholder seats on your particular train are gone, you will be asked to pay full price to ride the train. You can buy nicely discounted tickets in advance on the Thalys train.
Secondly, where will you be traveling in France? Here, you can buy heavily discounted tickets on the TGV lines in advance. Note that France also limits their seats on the TGV train to passholders. They also charge supplemental fees to ride their TGV trains. About 9Euro for each train.
The big secret here is to do more homework and planning on the different train systems, nail down your precise travel dates and buy tickets that you need in advance. The pass is just too easy an answer then enough detailed planning has not been done. We can help if you provide more detail on where you will be and when.