The Washington-bound United Airlines Boeing had taken off in Rome, the air force information service SIRPA said yesterday.
Airline officials declined to confirm or deny the incident when contacted by AFP.
The Rafale fighter aircraft reached the jet after a brief supersonic flight between the towns of La Roche-sur-Yon and Nantes near the Atlantic coast, where the radio contact was re-established. The passenger jet then pursued its course.
Firefighters in the area said they received a number of phone calls from alarmed residents after the fighter jet broke the sound barrier about 100 kilometres (60 miles) south of Bordeaux at a cruising altitude of 35,000 feet (10,700 metres).
Military officials said that in incidents such as yesterday's the pilot of the fighter jet would position himself to the left of the plane with the pilot of the jetliner in full view to identify the problem in line with international regulations.
Yesterday's incident followed "a normal procedure as is done dozens of times every year," SIRPA said. About 70 such situations were recorded last year.