Nobody was hurt in the incident which comes as France remains on high alert following a series of jihadist attacks that have claimed over 230 lives since January 2015. Prosecutors said they had launched an anti-terrorism investigation.
France goes to the polls on April 23 in the first round of a two-stage presidential election, in which security is one of the main issues on voters' minds.
The latest shooting also came on the second day of an official visit to Paris by Britain's Prince William and his wife Kate.
The incident took place at around 8:30am (0730GMT) in the Orly-Sud terminal at the smaller of Paris' two international airports, located south of the capital.
"A man took a weapon from a soldier then hid in a shop in the airport before being shot dead by security forces," an interior ministry spokesman told AFP. No-one was injured.
Addressing reporters at the airport Le Roux later said that the man had tried "but not succeeded" in grabbing the rifle of the female soldier on patrol with two male colleagues.
He was suspected of then stealing a car in another suburb and driving to Orly, Le Roux said. Police sources said he was aged 39.
A witness to the events at the airport told BFM TV he saw the man in possession of the soldier's rifle and threatening her.
"The soldiers were trying to reason with him," he said, adding that as he fled the scene he heard two shots.
"There are policemen, emergency workers and soldiers everywhere," he said after being forced to evacuate the terminal with around 3,000 others.
Air traffic to Orly was suspended and all incoming flights rerouted to Charles de Gaulle airport north of Paris.
Several planes that were preparing for takeoff or had just landed in Orly were grounded on the tarmac while the security operation unfolded.
France is still in a state of emergency after a series of terror attacks, including the November 2015 massacre in Paris and a truck attack in Nice, in July last year.
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