The 39-year-old, a repeat offender with convictions for receiving stolen goods, armed robbery and drug-trafficking, appeared to be ready "to go to the end", according to prosecutor François Molins, who is heading an anti-terror investigation.
During Saturday's attack Beglacem shouted "I am here to die for Allah. Whatever happens, there will be deaths!" before grabbing a soldier and seizing her assault rifle.
He was then shot dead by her colleagues.
Targeting soldiers "corresponds to the calls made by jihadist terrorist organisations", Molins commented on Saturday evening.
Belgacem, who is a French national of Tunisian origin, was reported to have been radicalised during a 2011-2012 jail term but a search of his home in 2015 revealed nothing of interest and he was not put on the government's anti-terror watch-list.
Drugs, drink, crime
Belgacem's father, interviewed by Europe 1 radio after being questioned by police overnight, insisted that his son had "never been a terrorist".
"He never prayed and he drinks," he said. "This is what happens under the influence of alcohol and cannabis."
The father, who has not been named in full by French media, said that his son phoned him on Saturday morning after firing a pellet gun at traffic police, slightly wounding one in the head.
"He was extremely wound up, even his mother couldn't understand him," he explained, adding that his son had asked for his forgiveness because he had "done something stupid".
"I said 'No I don't forgive you because you hit a gendarme'," the father told Europe 1.
Belgacem then went to a bar he used to frequent and fired in the air before stealing a car and heading for the airport.
A Koran, 750 euros, a packet of cigarettes and a cigarette-lighter were found on Belgacem's body and he threw a petrol can on the ground before the attack.
A search of his home found a quantity of cocaine as well as a machete.
A search of his parents' home revealed nothing relevant to the inquiry, police sources said.
His father and brother reported to police on Saturday morning and his cousin, who had met him in a bar on Friday evening, did so a few hours later.
The father was released on Saturday evening, while the other two men were still being questioned on Sunday to establish their relative's psychological state at the time of the attack.
Right-wingers attack government
Prime Minister Bernard Cazeneuve accused far-right presidential candidate Marine Le Pen of going too far after she told an election rally that the government was out of its depth in the face of "Islamist fundamentalism" on Saturday.
Mainstream right candidate François Fillon joined the fray later, claiming that France is "in a situation of quasi-civil war" and slamming Interior Minister Jean-Jacques Urvoas for saying that it might be possible to end the state of emergency instituted after the November 2015 terror attacks.
Air traffic from Orly returned to normal on Sunday after 178 flights were cancelled on Saturday.
About 100 people slept on camp beds at the airport overnight and airlines put up 100-200 in airport hotels.