That's what I intend to do.
Jetblue is pretty refundable, and I hope all of your nonrefundable bookings were somewhat refundable. Airfrance may pay you, but I can't imagine it'll be quick and easy.
Also, keep in mind that DOT only provides for coverage of cancellation fees for positioning flights, not the cost of the actual flights. That can be very low, and I wonder how DOT would rule if you aren't charged a fee but don't get a refund (only a credit)