KLM absolutely flew between JFK
and the Netherland Antillies up until the 1970s - DC8s were commonly used on these routes. Later, ALM
took over these routes.
During these years, other european carriers operated flights to other destinations, usually as a continuation of their transatlantic services; for example, AirFrance flew from JFK
to Guadalajara and Mexico City as a continutation of a Paris originating flight, BOAC had service from JFK
to several islands in the Caribbean plus Bermuda, and the like.
I remember travelling from New York to Guadalajara as a child on Air France flight 77, a very comfortable 707.