The Islamic State of Iraq and the Levant (ISIL) group claimed responsibility for the attack on Thursday evening, which took place three days before France's first round of presidential election.
The French often decide their presidents with two rounds of voting.
The man who shot a police officer dead and injured two others in Paris was not previously named in any French security watch list as a potential risk, officials said Friday.
The attack, which killed one police officer, could influence voters who will cast their ballots Sunday, analysts say.
Authorities said Cheurfi was released from prison in 2015 - and re-arrested again in February for threatening to kill police.
The Champs-Elysees, Paris' most iconic boulevard, was returning to its normal activities Friday, after a gunman killed one policeman and wounded two others on the world-famous street.
"The whole of Europe is targeted because it represents the values and ideals of peace", he said.
The candidates who could lose votes are centrist candidate Emmanuel Macron and far-left candidate Jean-Luc Mélenchon, who had seen a recent surge in polls, he said.
He was convicted in 2003 of attempted homicide in shootings on two police officers.
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Authorities are trying to determine whether "one or more people" might have helped the attacker, Interior Ministry spokesman Pierre-Henry Brandet told reporters at the scene of the shooting.
Police found a note defending Islamic State near his body and believe he had "opened fire on the officers in the knowledge he would be killed by them", a source close to the investigation told Reuters.
The attacker emerged from a vehicle and used an automatic weapon to shoot at officers outside a Marks & Spencer's department store at the center of the Champs-Elysees.
Le Pen too had earlier taken a characteristically tough stance against Islamic extremism, branding it a "barbaric and monstrous totalitarian ideology" and insisting France immediately take back control of its borders from the European Union.
In a statement from its Amaq news agency, IS gave a pseudonym for the shooter, Abu Yusuf al-Beljiki, indicating he was Belgian or had lived in Belgium.
The monitors from candidates were absent at four polling stations in the town of Remire-Montjoly in the overseas region of French Guiana at the time when the first round of the presidential election was set to begin and had to be replaced, local media reported on Saturday.
There were conflicting reports Friday morning of people who had been identified by the Belgian security services as being involved in the attack, and France remained on edge just days before key presidential elections.
Will the French election be the latest in a series of political events to shock the world? He also wants to give more power to parliament and stop the use of nuclear power, the source of almost 80 percent of France's electricity.
The terror group has claimed responsibility for the attack - giving the attacker a war name indicating he had ties in Belgium and praising him as a "fighter of the Islamic State", the Independent of the United Kingdom reported.
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