The 777-200, which was carrying 294 passengers from Paris to Vancouver, was diverted to Prestwick after taking off at 10:57 on Saturday.
The airline said the plane landed "normally" at 13:20 local time.
Air France added that it had sent a second aircraft to Prestwick in order to fly the passengers back to Charles de Gaulle Airport on Saturday.
In a statement, it said: "Air France confirms that flight AF374 operating from Paris CDG to Vancouver on 15 July, 2017, was diverted to Glasgow Prestwick where it landed normally.
"Following the appearance of a slight smell of burning on board, the cabin crew, trained for this kind of situation, took the necessary precaution and diverted to the closest airport."
An Air France passenger jet has made an emergency landing at Prestwick Airport after fumes were detected on board.