The reservist, said to be in her 20s, fought back and the man forced her to her knees as he attempted to wrest her Famas assault rifle from her.
Two colleagues on the soldier's patrol shot and killed the man before he could fire the military-grade weapon in the busy airport terminal.
The man, who was known to police and intelligence services, then proceeded to hijack a vehicle at gunpoint in another nearby suburb, Le Roux added, before continuing on to Orly, where he grabbed an assault rifle from a security officer on duty. "I've screwed up with a police officer'".
Interior minister Bruno Le Roux said the man was linked with a carjacking earlier in the morning in a northern Paris suburb and that police and intelligence services know who he is. However, The Associated Press was told by the Paris prosecutor's office that the attacker was a 39-year-old male with a history of robbery and drug offenses, and was not on any database as a threat to national security.
One neighbour, Hamid, said: "The last time I saw him was three days ago". Flights were diverted and passengers on planes were not allowed to disembark. "We went down the stairs and right after we heard two gunshots".
By Sunday afternoon air traffic had returned to normal, a spokeswoman for the Paris airports authority said.
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The officer who was attacked was part of a special unit called Sentinelle, which was created in the wake of the terrorist attacks in 2015, the AP reports.
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". Nobody else was injured, officials said. In 2015, his home was searched but nothing suspicious was found.
According to police, the man did not have any accomplices and no explosive devices were found at the airport.
Orly - located 13km south of Paris - is the capital's second-largest airport.
The operation involves some 7,000 troops of whom roughly half are deployed in the Paris region.
The attack, which follows a similar incident in early February outside the Louvre museum in Paris, comes in the middle of a fiercely-contested presidential race between a centrist candidate, Emmanuel Macron, and a far-right-wing candidate, Marine Le Pen, who has made anti-terrorism and anti-immigration the centerpieces of her campaign.
The incident is one in a string of attacks on France, including a series of gun attacks in November 2015 that left 130 dead, and in Nice a year ago when a lorry ploughed into crowds at a Bastille Day celebration killing 86. He was shot and wounded and taken into custody.