Update 10.50am: A man has been shot dead after grabbing a gun from a female anti-terror officer at Orly Airport in Paris.
The French Interior Minister said he was a radicalized Muslim and was already known to intelligence services.
Authorities say earlier, the man shot and injured a traffic officer, before escaping and driving to the terminal in a stolen car.
The airport has been evacuated, and flights are being diverted to Paris' other airport - Charles de Gaulle.
Update 9.55am: Police in Paris are linking two shootings that took place in the city this morning, one at a police checkpoint and one at Orly Airport.
French police shot dead a man at Orly Airport after he grabbed a soldier's gun, while a traffic officer was injured in the earlier incident.
Passengers at Orly described gunshots and panic.
A witness identified only as Dominque said on BFM television: "The soldiers took aim at the man, who in turn pointed the gun he had seized at the two soldiers."
Another man said a group of three soldiers were targeted, and they tried to calm the man who had seized the weapon. Then the man said he heard two gunshots.
Another witness, identified as Patrick, said he was at the check-in counter when he saw someone come in from outside and the incident began.
A French journalist on a flight that landed from Nice told France-Info radio that passengers were being kept on the plane.
Britain's Duke and Duchess of Cambridge are on the second day of their trip to Paris where they will meet victims of the Bataclan and Nice terror attacks later.
Update 9.10am: A man has been shot dead by the security forces at Orly airport in Paris - after stealing a soldier’s gun.
The man ran into a shop at the south terminal with the weapon, but was shot a short time later.
The airport has been evacuated and SWAT teams have been sent in.
Counter terrorism police are now searching the airport for explosives. There are reports the man may have had an accomplice.
In a separate incident, a policeman has been shot at a traffic checkpoint north of Paris.
It is unclear if the two events are related.
Earlier: A man has been shot dead after trying to seize the weapon of a soldier guarding Orly Airport in Paris, police said.
The soldier is part of the Sentinel special force deployed around France to protect sensitive sites after a string of deadly Islamic extremist attacks.
Police evacuated part of the airport and warned visitors in a tweet to avoid the airport while the police operation was under way.
The shooting on Saturday morning came after a similar incident last month at the Louvre Museum. France remains under a state of emergency.
The Sentinel force includes 7,500 soldiers, half deployed in the Paris region and half in the provinces.
Orly is Paris's second-biggest airport behind Charles de Gaulle, serving domestic and international flights, notably to destinations in Europe and Africa.
