The woman, 57, was struck by bullets as she drove by with her husband on a rented scooter at around 8pm on Sunday.
The gang using AK-47s killed three people including the tourist in a bloodbath at a petrol station in Ollioules, close to Toulon in the south of France.
Two unnamed men, aged 29 and 30, with criminal records, were also killed.
The woman’s husband suffered injuries in the shooting.
An investigating source reportedly said: “The couple was in the wrong place at the wrong time.
“They had hired a scooter and ended up in a gangland shooting.
“The woman was hit in the back and died, along with two men who were known to police as being involved in the drugs trade.
“The woman’s husband was driving the scooter and hit in the shoulder by a bullet and is currently in hospital in Toulon.
“The woman was on the back of the scooter and was hit from behind.”