The married father-of-one, who has not been named, was stabbed in the throat, lung and chest, it is believed.
At least two of the wounds were thought to have been fatal.
The area where he was found could only be accessed with an ID badge or accreditation.
Prosecutors have begun a murder investigation to find out how the attack on the senior controller happened.
The 34-year-old victim is believed to have worked at the airport, near the eastern city of Mulhouse, on the border with Germany and Switzerland, since 1988.
Investigators do not think the attack is related to terrorism and are believed to be investigating motives related to his personal life or job.
Police have not made any arrests yet and are still looking for the murder weapon, reported newspaper L'Est Republicain.
Flights in and out of the airport have not been affected.