Well, as of now, all CDG-JFK are operated by AirFrance (Delta dropped that route in exchange for picking up slots at LHR). I have heard DL should be getting it back soon, but in the meantime DL has resorted to AF codeshares. I would try AF. I have found them to be fine for longer-haul flights. Intra-europe, they leave a lot to be desired (granted, it's been some time since I've done an AF intra-EU flight, but from what I've heard, my characterization still stands true), but the inconvenience of connecting on LH makes AF the right choice, in my eyes.