It's hard to predict when seats are going to be taken up. There's probably other people looking to book awards to Paris from NY, too, besides yourself. It's a race to see who does it first.
You can try exploring different routes, and then booking them, and change to a non-stop if you find availability. Keep in mind that it there is a change fee to move dates if you don't have status, and a fee to move cities if you use MileSAAver awards.
This link has the particulars and details:
Making Award Reservations