The driver of the truck, Mohamed Bouhlel, had one criminal conviction for road rage
The man who drove a lorry into a crowd in Nice is believed to have gone to the scene twice in his rented truck before the attack.
The news came from a judicial source as two more people were arrested over the Bastille Day atrocity which claimed at least 84 lives.
Mohamed Bouhlel, a 31-year-old Tunisian who had lived in the French city for a number of years, mowed down revellers who gathered on the promenade for a fireworks display on Thursday night.
Bouhlel, who was shot dead by police after the attack, is thought to have made trips to the site on the two days leading up to the massacre.
A man and a woman were held in Nice on Sunday morning and their arrests follow the detention of five other people since the tragedy - including Bouhlel's ex-wife.
Authorities are trying to determine if he acted alone - but the country's prime minister has said he had been radicalised quickly.
Several people, among hundreds who have been questioned, said Bouhlel showed signs of being religious, according to the judicial source.
But some of his friends and relatives have claimed he smoked, drank and never visited mosques.
Jihadist group Islamic State has said the lorry driver was one of their "soldiers".
Officials have yet to produce evidence that Bouhlel had any links to IS.
However, PM Manuel Valls said there was no doubt about the Tunisian's motives.
Speaking in an interview with Sunday newspaper Le Journal du Dimanche, Mr Valls said: "The investigation will establish the facts, but we know now that the killer was radicalised very quickly."
"The claim on Saturday morning by Islamic State and the fast radicalisation of the killer confirms the Islamist nature of this attack."
He added: "Daesh (IS) gives unstable individuals an ideological kit that allows them to make sense of their acts...this is probably what happened in Nice's case."
Mr Valls warned that there was no risk zero and new attacks would occur.
"I've always said the truth regarding terrorism: there is an ongoing war, there will be more attacks. It's difficult to say, but other lives will be lost."
On Saturday, Interior Minister Bernard Cazenueve on Saturday called on "patriotic citizens" to become reservists to help relieve exhausted security forces.
But the measure appears to have done little to temper concerns among opposition politicians who are asking how a country still under a state of emergency since the November Paris attack could have let this happen again.
Highlighting the "serious deficiencies" in protecting French citizens, National Front leader Marine Le Pen called on Mr Cazeneuve resign.
"Anywhere else in the world a minister with such a terrible record - 250 deaths in 18 months - would have resigned a long time ago," she told reporters.