Update 9.30pm: Officials in Paris say a gunman who was shot dead at Orly airport went there with a "clear intention of killing people".
The 39-year-old, who tried to grab a female soldier's weapon, was known to police and intelligence services.
Paris prosecutor Francois Molins said the man who struck at Orly Airport had a 9mm revolver that shoots birdshot and used it to take the soldier hostage.
Mr Molins said the attacker shouted that he wanted to die in the name of Allah and "whatever happens, there will be deaths".
He said the soldier's colleagues shot the man dead after he wrenched away her powerful military-grade assault rifle on Saturday morning.
Mr Molins said French soldiers fired three bursts, eight rounds in all, to kill the attacker. He said the attacker held a pistol to the soldier's head and used her as a shield.
Mr Molins said the attacker wanted to use the soldier's assault rifle to shoot people at the busy Paris airport. He said the attacker also carried a container of petrol that he threw to the ground.
Speaking at a news conference, the prosecutor said a Quran was among the items later found on the body of the attacker.
He said the 39-year-old was flagged for suspected radicalism during a previous spell in prison.
Mr Molins said the attacker - a Frenchman he named as Ziyed Ben Belgacem - had fired the pistol twice earlier that day: once against French police at a traffic stop, then in a bar where he pointed it at customers but did not hit anyone.
The prosecutor said a cousin of the airport attacker is in custody after presenting himself to police. The attacker's father and brother are also in police custody for questioning, standard operating procedure.
Update 6pm: French media have named the man shot dead at Orly airport south of Paris as Ziyed B, and say that he was known to security services.
Officials say the 39-year-old died after trying to wrestle a rifle from a female soldier.
He had been stopped earlier elsewhere in the city.
Soldiers at Paris's Orly Aiport have shot dead a man who wrestled one of their colleagues to the ground and tried to steal her rifle, officials said.
Thousands of travellers were evacuated and at least 15 flights were diverted to the city's other airport, Charles de Gaulle. No-one else was hurt in the incident.
Police did not immediately provide a motive or identify the attacker, but the Paris prosecutor's office said he was 39 and had a record of robbery and drug offences.
The office said he did not appear in a French government database of people considered potential threats to national security.
Earlier on Saturday, he had fired birdshot at officers during a traffic stop in a Paris suburb, wounding one in the face, then stole a woman's car at gunpoint. It was found later near Orly.
The prosecutor's office said its anti-terrorism division is handling the investigation and has taken the attacker's father and brother into custody for questioning.
The incident further rattled France, which remains under a state of emergency after attacks over the past two years that have killed 235 people.
Defence minister Jean-Yves Le Drian said the attacker assaulted three soldiers patrolling the airport. He said the soldier who was attacked managed to hold on to her rifle and the two others she was with opened fire to protect her and the public.
A spokesman for the force later said that she was shocked but not hurt.
It happened in a public area of the airport's South Terminal, before passengers show tickets or go through security.
Officials said about 3,000 people were evacuated from Orly, where passengers told of gunshots and panic.
People on 13 flights that landed around the time the drama was unfolding had to stay on planes for several hours. Augustin de Romanet, president of the ADP airport authority, said they were allowed off around noon, once a search of the airport was complete.
A witness identified only as Dominque told BFM Television that the attacker held the soldier by the throat and held her arm and her weapon.
"We saw it was a serious situation so we escaped," he said. "We went down the stairs and right after we heard two gunshots."
Taxi driver Youssef Mouhajra was picking up passengers at Orly when he heard shots, which he first thought were just a warning.
"We have become accustomed to this kind of warning and to having the soldiers there," he said.
Then he said he saw people rushing out of the terminal.
"I told (the passengers) 'let's get out of here'," he said. As he drove away, he saw soldiers and police rushing towards the airport.
The soldier who was attacked is part of the Sentinelle special force deployed around France to protect sensitive sites after a string of deadly Islamic extremist attacks. The force has 7,500 soldiers, half deployed in the Paris region and half in the provinces.
Saturday was at least the fourth time Sentinelle soldiers have been targeted since the force was created. It was set up after the January 2015 attack on satirical magazine Charlie Hebdo and reinforced after the assaults that left 130 people dead in Paris in November that year.
Orly is Paris's second-biggest airport, behind Charles de Gaulle. It has domestic and international flights, notably to destinations in Europe and Africa.
The shooting comes after a similar incident last month at the Louvre Museum in which an Egyptian man attacked soldiers guarding the site and was shot and wounded.