There are two very good one way low fares that match up well together for a cheap round trip ticket from New York JFK to Europe priced in the mid-$300s to $400s round trip. Star Alliance airline TAP Portugal has one way fares to many cities around Europe priced in the $310s. There are several cities where a similar TAP Portugal fare is available for the return flight for around $600 round trip.
Norwegian Airlines has many cities in Europe with one way ticket prices to New York JFK priced under $200 one way. There are many potential destinations in Europe for under $500 round trip from New York JFK to countries across Europe by flying TAP Portugal outbound from New York and Norwegian or some other discount airfare back from Europe to New York.
Personally I like Norwegian Airlines. The seat and bag fees are very high, but the overall ticket price generally falls lower than the competition and the aircraft are mostly first rate for economy class travel on the few transatlantic flights I have made on the airline. Their bag and seat fees are far more reasonable for intra-Europe flights compared to the $90+ for USA flights. The good aspect of this deal with the return flight from Europe to New York JFK on Norwegian is that direction incurs bag and seat fees about one-third less than the flight from New York to Europe. Generally about $60-$70 for checked bag and seat and meal for Europe-USA flight.
Google Flight Maps TAP Portugal one way Saturday April 1
TAP Portugal New York JFK to:
TAP Portugal New York JFK – Lisbon LIS – Venice, Italy VCE
Overnight layover in Lisbon from 11:30am to 8:20am next day for two countries on one fare.
Norwegian Airlines Venice VCE – Stockholm ARN
$73 USD / 65.30 EUR one way Tue Sep 27
Norwegian Airlines Stockholm ARN – New York JFK
Norwegian fares are lower in later months. This is just one example of how a return trip can be found at a comparable price on Norwegian one way back to USA for the same price as a TAP Portugal round trip ticket.
For these same dates Sep 19-27, you can fly Turkish round trip for $609 or TAP Portugal for $612. Other cities and other dates will be a lower overall ticket price combining TAP and Norwegian.