It looks like there are some JFK-PMI dates on Google Flights for $461 on Skyteam. September 8-13 is one example. It doesn't actually book for that price on Delta or Air France, but looks like it can be booked on KLM. There are a few dates available with some different routings.
September 8-13 looks like it is JFK-ORY-PMI on AF and Air Europa with a return on Air Europa and Delta through Madrid and ATL. If the Matrix is to be believed, there is an all KLM option available October 4-10 for $461, through Madrid on the way out and Amsterdam on the way back. Fare code VLPW3US.
Not too bad honestly though you start getting into the wetter and cooler months that late.