Flight AF022 landed at JFK airport without incident and on schedule, and was later taken to a special area of the airport for a security check, an Air France official in Paris said.
The threat was made by telephone from the United States, the Air France official said.
Pentagon officials were not immediately available for comment following the incident, which occurred as the United States marked its Memorial Day holiday.
The fighter jets were American, US media said, quoting an agency called the Maryland Coordination and Analysis Center.
It co-ordinates federal, state and local agencies in the gathering and analysis of intelligence information. — AFP.