Finnair nonstop flights between New York JFK and Helsinki, Finland are as low as $330 round trip for flights in September.
Prices go up for October to December, but still a great fare at $385 round trip.
This fare is bookable through several Oneworld Alliance airlines, however, there seems to be a British Airways booking glitch as I write this post (no AARP fares are coming up).
American Airlines link was bookable through Google Flights as I searched this fare.
Google Flights appears to have a faulty direct link issue for Finnair flights. I usually get an error message when trying to link from Google Flights to Finnair tickets this past month.
A better value for earning frequent flyer miles with this ticket is go directly to Finnair.com and search your dates.
Finnair coded flights in economy O class earn 50% Alaska Mileage Plan miles for 4,117 frequent flyer miles.
Finnair New York JFK – Helsinki HEL – New York JFK