The airport was evacuated at around 8.30am on Saturday after the man was shot dead by soldiers.
Interior Minister Bruno Le Roux said the man had tried “but not succeeded” in his bid to grab the rifle of the female soldier who was on patrol with two male colleagues.
Later on Saturday it was revealed that the man was already known to intelligence services, and had shot at a police officer earlier in the morning in the northern suburbs of Paris.
The officer escaped with only light injuries to the head during the shooting in Stains (marked in the north of Paris below).
No one was wounded in the airport incident.
Flights were suspended for Orly South and West terminal, with police urging the public to avoid the airport.
By mid afternoon air traffic was slowly getting back to normal.
As for the attacker, police sources say he was a 39-year-old Frenchman with several previous convictions, including for drugs and armed robbery, who was being sought by police.
His home was searched in 2015 after he was “detected as having been radicalised” but no incriminating evidence was found, the sources said.
French Interior Minister Bruno Le Roux confirmed he was “known to the police and the intelligence services”.
Witnesses reported panic at the airport at the time of the shooting.
“We had queued up to check in for the Tel Aviv flight when we heard three or four shots nearby,” witness Franck Lecam said.
“The whole airport has been evacuated,” the 54-year-old said, confirming what an airport worker, speaking on condition of anonymity, had said earlier.
“We are all outside the airport, about 200 metres from the entrance,” Lecam said.
“There are policemen, emergency workers and soldiers everywhere in all directions. A security official told us that it happened near gates 37-38 where Turkish Airlines flights were scheduled.”
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. In mid-February, an Egyptian staged a machete attack in Paris's Louvre museum before being shot and wounded.
The latest shooting comes weeks ahead of the first round of France's two-stage presidential election, in which security is one of the main issues on voters' minds.