A man who attacked soldiers at Paris Orly Airport carried a petrol can and shouted he was there to "die for Allah", Paris prosecutor Francois Molins said.
According to testimony of soldiers who witnessed the attack, the assailant put his air gun to the head of a woman soldier and shouted to other soldiers with her: "Put down your guns. Put your hands on your head. I am here to die for Allah. In any case, there will be deaths."
The attacker, who Mr Molins named as Zied ben Belgacem, was shot dead by the other soldiers. Mr Molins said three people were being held in police custody.
He said Belgacem's choice of target and evidence that he had been radicalised justified launching a terrorism investigation.
The man was known to police and intelligence services, Interior Minister Bruno le Roux told reporters on Saturday.
The busy Orly airport south of Paris was evacuated and security forces swept the area for bombs to make sure the dead man was not wearing an explosive belt.
However nothing was found, interior ministry spokesman Pierre-Henry Brandet told Reuters.
No one else was injured at the airport.
Flights were suspended from both terminals and some flights were diverted to Charles de Gaulle airport north of the capital, airport operator ADP said.
Earlier, a police officer was shot and wounded by the same man during a routine traffic check in Stains, north of Paris.
The incidents came five weeks before France holds presidential elections in which national security is a key issue.
The country remains on high alert after attacks by Islamic State militants killed scores of people in the last two years - including co-ordinated bombings and shootings in Paris in November 2015 in which 130 people were killed.
A state of emergency is in place until at least the end of July.