The 40-year-old shot at police officers manning a checkpoint in northern Paris before launching the airport attack, the French interior minister said.
Terrorism prosecutors have opened and investigation into the assault, which comes after a series of Isis-inspired attacks across France.
The first shooting came at around 7am local time (6am GMT) in Stains, when a man was stopped by police at a security checkpoint.
"It turned bad and the individual shot at the officers before fleeing,” a police source told Reuters.
“This same man - a radicalised Muslim known to intelligence services and the justice system - then took a Famas (assault weapon) from a soldier at Orly's southern terminal ..before being shot dead by a soldier.”
The car stopped in Stains was a Renault Clio, which was later abandoned for a Citroen Picasso hijacked at gunpoint.
Reuters also reports that no explosives were found on his body