Investigators are still trying to understand what motivated Saturday's assault by 39-year-old Ziyed Ben Belgacem, which led to a major security scare and the temporary closure of the capital's second-busiest airport.
"Toxicology tests carried out on Sunday showed an alcohol level of 0.93 grams per litre in his blood, and the presence of cannabis and cocaine," the source said.
Ben Belgacem's father had insisted earlier Sunday that his son was "not a terrorist" and that his actions were caused by drink and drugs.
Ben Belgacem, who was born in France to Tunisian parents, grabbed a soldier on patrol at Orly's southern terminal on Saturday morning. He put a gun to her head and seized her rifle, saying he wanted to "die for Allah".
The attacker, who had also fired at police in a northern Paris suburb earlier that morning, was shot dead by two other soldiers after a scuffle.
Ben Belgacem's father insisted his son -- who had spent time in prison for armed robbery and drug-dealing -- was not a extremist.
"My son was not a terrorist. He never prayed, and he drank," the father, who was in shock and whose first name was not given, told Europe 1 radio.
Investigators were examining his telephone.
The attack at Orly comes with France still on high alert following a wave of jihadist attacks that have claimed more than 230 lives in two years.
The violence has made security a key issue in France's two-round presidential election on April 23 and May 7.
- Not on terror watchlist -
Ben Belgacem's brother and cousin were released Sunday after they, like the attacker's father, were held for questioning. All three had approached police themselves on Saturday after the attack.
After spending Friday night in a bar with his cousin, Ben Belgacem was pulled over by police for speeding in the gritty northern Paris suburb of Garges-les-Gonesse, where he lived, just before 7:00 am.
He drew a gun and fired, slightly injuring one officer. Shortly after, he contacted his relatives to tell them he had "done something stupid", they told police.
Ben Belgacem later appeared at the bar where he had been the previous night, firing more shots and stealing another car before continuing on to the airport.
He had been investigated in 2015 over suspicions he had radicalised while serving jail time, but his name did not feature on the list of those thought to pose a high risk.
Paris prosecutor Francois Molins said Ben Belgacem appeared to have become caught up in a "sort of headlong flight that became more and more destructive".
Dozens of flights to and from Orly were cancelled during an hours-long shutdown after the incident, but by Sunday afternoon air traffic had returned to normal, a spokeswoman for the Paris airports authority said.
The shooting took place on the second day of a visit to Paris by Britain's Prince William and his wife Kate, which was unaffected.
- 'I've screwed up' -
Ben Belgacem's father told Europe 1 his son had called him after the first police shooting "in a state of extreme agitation".
"He said to me: 'Daddy, please forgive me. I've screwed up with a police officer'."
At the time of his death, Ben Belgacem was carrying a petrol can in his backpack, as well as 750 euros ($805) in cash, a copy of the Koran, a packet of cigarettes and a lighter.
A small amount of cocaine and a machete were found during a search of his home on Saturday.
Soldiers guarding key sites have been targeted in four attacks in the past two years but escaped with only minor injuries.
In mid-February, a machete-wielding Egyptian man attacked a soldier outside Paris's Louvre museum, injuring him slightly, before being shot and wounded.
President Francois Hollande said Saturday his government was "determined to fight relentlessly against terrorism".