Two French officials have said that the Champs-Elysees gunman was detained in February for threatening police.
The officials - who spoke on the condition of anonymity - said the gunman was detained at the end of the month after speaking threateningly about the police, but later released due to a lack of evidence.
They also reported he was convicted of attempted homicide in 2003 in shootings on two police officers.
A man believed to be the principal attacker was shot dead at the scene, after a police officer was killed and two others seriously wounded.
A second man wanted in connection to the attack is reported to have handed himself into police.
The attack comes just days before France's presidential elections.
The gunman killed in a suspected terror shooting on the Champs-Élysées in Paris was a French national, Belgian's interior minister has told the nation's public broadcaster VRT.
"The investigation is continuing. What we can confirm is that the perpetrator was a French national," Jan Jambon said.
Islamic State militants, who had claimed being behind the attack in which a French policeman was shot dead, had named the attacker as Abu Yousif al-Belgiki.
The naming - via its Amaq news agency - translates as "the Belgian" in Arabic.
French police are believed to have detained three family members of the gunman killed in the suspected terror shooting on the Champs-Élysées in Paris.
Officials earlier said the main suspect in the shooting of three police officers - one fatally - was a 39-year-old man from the same suburb.
A man hunted in connection with a suspected terrorist shooting on the Champs-Élysées in Paris has reportedly handed himself in to police.
The Belga news agency said the man surrendered to Antwerp police.
A spokesperson for the French interior ministry, quoted by Europe 1 radio, earlier said the wanted man had been flagged to French police by Belgian security services.
His nationality was not known.
France will ramp up security to protect the public during voting in the French presidential elections in the wake of the Champs-Élysées attack.
French Prime Minister Bernard Cazeneuve said nothing will stop Sunday's elections as he confirmed the government had fully mobilised its security forces, including elite units, to bolster the 50,000 police already on duty.
Thursday evening's fatal shooting of a policeman in Paris came with only days to go until Sunday's national poll - the first round of the two-round election.
Two officers injured by an armed attacker are both out of danger, French officials said.
Interior Ministry spokesman Pierre-Henry Brandet said one of the injured officers was more gravely hurt than the other but both are doing better.
French police are reportedly hunting for a second man in connection with a suspected terrorist shooting on the Champs-Élysées in Paris.
A spokesperson for the French interior ministry, quoted by Europe 1 radio, said the wanted man was identified by Belgian security services.
Pierre-Henry Brandet said the second suspect was wanted in connection with the killing of a policeman in a shooting in which an attacker was killed.
France's anti-terrorism prosecutor has confirmed that a foreign tourist was injured in the Paris shooting.
Francois Molins said "a female foreign tourist was wounded" as reports suggested the unnamed woman had been injured by fragments from the gunshots.
World leaders have been sending their condolences and messages of support to those in France after an armed assailant opened fire on three police officers - killing one and seriously injuring the other two - in Paris.
Australian prime minister Malcolm Turnbull offered his country's prayers for the police officers who were shot as he urged Australian travelers to check for security warnings and be vigilant about their safety.
While U.S. Vice President Mike Pence said Thursday's shooting was the "latest reminder that terrorism can strike anywhere, anytime" as he sent condolences and prayers to all those caught up in the attack.
The main suspect in the shooting of three police officers on the Champs-Elysees is believed to be a "39-year-old man from a suburb east of the French capital", according to officials.
Police officials also told the Associated Press that a home in an eastern suburb of Paris that was believed to be linked to the attack had been searched in the wake of the shooting.
Police raids are under way in Paris after an armed attacker shot three police officers on the Champs-Elysees.
France's anti-terrorism prosecutor Francois Molins confirmed searches were being carried out in the capital and said that investigators had already verified the identity of the gunman but were trying to determine whether he had accomplices.
He said: "The identity of the attacker is known and has been checked. I will not give it because investigations with raids are ongoing."
Officials confirmed that at least one location in the eastern Paris suburbs was being searched early Friday.