I would like to know the CHEAPEST way to go from Amsterdam to Paris. But it don't need to be straight, only cheap.
For example, I have no problem to make a tour from Amsterdam until reach Paris.
The cheapest way to travel from Amsterdam to Paris is by hitch-hiking.
Failing that, early-booked buses are cheapest. For example, if I search now for a Eurolines bus on a weekday late May, I find tickets as cheap as 9€. You want to search for Promo tickets, indicated in dark red in the fare calendar.
Screen-capture of Eurolines booking system
There are probably other bus companies, but probably it won't get much cheaper than that.