I don't think there's a perfect solution to this. First, I wholeheartedly agree on avoiding CDG. It's a mess.

Unless you're looking to to get a flying start on a status run with *A or OW, this leaves KL, CO or DL.

While the DL option probably looks good on paper, I'm inherently hesitant to connect through an east coast "hub" especially when my onwards flight is a once-a-day TATL. (I'm guessing DL doesn't fly several times a day to NCE). Any type of NY-area air traffic delays can cause you to miss your JFK-NCE flight and possibly be stranded for a day, or best case be re-routed somewhere through Europe.

CO's BF is a better product than KL's business class. But remember that the BF seat is different between the 777 that serves CDG/LGW and the 767's that serve AMS. An option to catch the 12:10 AMS-NCE flight that rk mentions is to catch CO58 IAH-AMS on the days that it operates. (dep 3:30pm, arr 8:20am, still 4 hours at AMS mind you)

Let us know how you decide to go