Icelandair has a low fare of $499 from New York JFK to Paris CDG on about 20 dates between January and April 2016 with many more dates at $560 round trip. This is a one-stop flight via KEF Keflavik Airport in Iceland.
Norwegian has some dates with $449 fares, however, checked bag fees are extra on Norwegian and Icelandair allows two free checked bags.
Icelandair New York JFK – Keflavik KEF – Paris CDG
$498.80 Tuesday January 26 – Wednesday February 3, 2016
Note: This books in Icelandair deep discount economy N class and is an ineligible booking code for earning miles with Alaska Airlines Mileage Plan.
Compared to the fares on the legacy airlines pricing over $1,100 round trip, this Icelandair fare really stands out for an April 5-15 trip.
My trip to Sacre Couer, Montmartre, Paris in late September 2015.