The unit attacked at the airport was part of Operation Sentinel, which involves about 7,000 soldiers who patrol public areas in France, including high-profile locations like airports, areas near large tourist attractions and train stations.
The attack occurred shortly after the man shot at a police officer during a routine traffic stop in a Paris suburb, the French interior minister said.
Earlier that day he had been involved in a shooting and then a carjacking. No one was injured.
Ben Belgacem later appeared at the bar where he had been the previous night, firing more shots and stealing another vehicle before continuing on to the airport.
According to the soldiers, the attacker yelled: "Put down your weapons!"
"Put your weapons down, hands on your heads". I am here to die for Allah.
Molins told reporters thata container filled with petrol was found in the dead man's backpack, along with a Koran, some cigarettes and a lighter. He held a gun to her head and, contrary to earlier reports, managed to wrest her assault rifle away from her. Molins said video surveillance footage appeared to show that Belgacem was "determined to see the process through to the end".
"The two minutes [of confrontation] with the soldiers demonstrate quite clearly the very strong determination of the attacker", Mr Molins said.
Molins said the assailant meant to open fire on the crowd of travelers.
He said he wanted to "die for Allah", and a scuffle between him and two other soldiers ensued, which resulted in him being fatally shot. "This is what happens under the influence of drink and cannabis", he said.
Witnesses described panicked bystanders fleeing, flights halting, traffic chaos and planes under lockdowns. He added, that he then saw people rushing out of the airport terminal.
The airport was evacuated as an elite operations unit and bomb squad officers rushed to the scene.
Flights were suspended for several hours.
Orly is Paris' second-biggest airport behind Charles de Gaulle, serving domestic and worldwide flights, notably to destinations in Europe and Africa.
Despite the transportation chaos, French authorities stressed that security planning - reinforced across the country in the wake of repeated attacks - worked well.
Belgacem's brother and cousin, who also came forward for questioning Saturday, are still being quizzed by anti-terror investigators.
Police found a small amount of cocaine during a search of Belgacem's flat, according to Molins.
Belgacem's father and brother were both arrested yesterday and taken into custody by French authorities, his father was later released.
He also had 0.93 grams of alcohol per liter of blood when he died Saturday, the prosecutors' office said.
Belgacem's plans were unclear, Molins said, adding that an investigation is meant to determine whether he acted as a "lone wolf".
He said Belgacem's choice of target and evidence that he had been radicalized justified launching a terrorism investigation.
Following the coordinated attacks around Paris in November 2015, the French government declared a state of emergency that was extended in December for the fifth time and will remain in force until July 2017.