The man shot dead after attempting to steal a soldier's gun at Paris Orly Airport on Saturday was a "radicalised Muslim" known to security services and was also involved in another shooting incident hours earlier in the day, French authorities said.

Security forces opened fire, killing him during the attack at the airport, the Telegraph reported.

The attacker assaulted a patrol of three soldiers including a woman, who he wrestled to the ground as he tried to grab her weapon at the airport, French Defense Minister Jean-Yves Le Drian said.

Two other soldiers then opened fire "to protect her" and the public at the airport.

French Interior Minister Bruno Le Roux said at a press conference that the man was known to the police and intelligence services. 

The man had earlier fled the suburb of Stains on Saturday in a car stolen from a woman at gunpoint after opening fire on officers, injuring one, during an identity check. 

The car was later found abandoned. According to one report, it contained a bloodstained T-shirt.

Meanwhile, Paris Orly Airport was evacuated while it was searched by bomb disposal squads. No explosives were found, said the report. An investigation was underway while the airport remains under maximum security alert. 

Some 3,000 people were escorted out of the airport terminals. Passengers in planes that had landed before the shooting were being kept aboard the aircraft until the airport was declared secure, said the officials. 

The CEO of Paris Airport Operator said Orly's south terminal, where the incident occurred, may remain closed until Saturday night. The airport's west terminal may reopen soon.

This was the fourth attack against security forces deployed as part of France's Operation Sentinel, said the French defence minister. The national security operation was launched following the Paris terror attacks in January 2015.

The French interior minister praised the swift response of security forces at the airport.

The incident came as the Duke and Duchess of Cambridge, Prince William and Catherine Middleton, were in Paris to meet survivors of the Bataclan attacks. 

The airport, the second largest serving the French capital, is about 20 miles from the central Paris residence of the British ambassador where the royal couple are staying, the Telegraph report said.

The couple, who began a two-day visit to Paris on Friday, were to attend a France-Wales rugby match later on Saturday as well as meeting victims of the 2015 Paris terrorist attacks at the Invalides military museum complex in the centre of the capital.

A police spokesman said they were being closely guarded.

France remains under a state of emergency declared after the 2015 attacks. Armed police and soldiers routinely patrol the streets of Paris, airports and railway stations.

The soldier whose gun was seized by the unidentified man at Orly Airport was part of a special counter-terrorism patrol.

The airport incident revived memories of a machete attack on soldiers at the Louvre museum in February. The attacker, a 29-year-old Egyptian, was shot by a soldier.