You can also do a JFK-CDG daytime run on BA if you are so inclined. The earliest flight from JFK-LHR gets in about an hour before the last LHR-CDG flight departs. BA allows the booking on their website, although you would be hauling butt through the airport trying to catch the CDG flight. This would be one of those booking where the stars would have to be in line. I can't imagine that the transfer point at T4 would be that much of a zoo at this time of night.