French President Francois Hollande said investigators will determine whether the Orly Airport attacker "had a terrorist plot behind him.''
Authorities said soldiers fatally shot the man after he wrestled one of their colleagues to the ground and tried to steal her rifle earlier Saturday.
According to the Paris prosecutor's office, the 39-year-old suspect, identified as Ziyed Ben Belgacem, was on authorities' radar for suspected Islamic extremism and his home was part of a massive search following the deadly Paris attack in 2015.
Officials also said the same man earlier fired bird shot at police officers during a traffic stop before speeding away and heading for the airport south of Paris.
Thousands of people were evacuated from the airport, and flights were redirected as a precaution.
The soldier whose weapon was seized is a member of a special force installed around France in the wake of a string of deadly terror attacks.