SkyTeam Alliance member Alitalia has New York JFK to Frankfurt via Rome FCO on sale for $531 round trip for departures from early September to end of March 2017. This ticket price has many available dates. Star Alliance has $608 to $633 fares from November to March.
Alitalia New York JFK – Rome FCO – Frankfurt FRA – Rome FCO – New York JFK
Good fare to Frankfurt.