"We don't understand why Islamic State has identified the wrong person", said a police source. The armed assailant shot and killed one officer, and injured two others.
He was shot dead in return fire while trying to escape, police sources said.
BFMTV reported on Thursday that the attacker was 39 and he was known to the French General Directorate for Internal Security (DGSI) for his "radicalization".
Paris: Security concerns took centre stage on Friday in the last days of France's tight presidential race as candidates defended their stance on the fight against terror in the wake of a shooting in Paris which killed one policeman.
With a record number of voters still undecided, analysts say the shooting could play into the narrative pushed by the far-right.More news: Crowd trouble delays Europa League match in Lyon
He was also convicted in 2003 of attempted murder in the shooting of two police officers.
Left-wing insurgent Jean-Luc Mélenchon warned against allowing panic to "interrupt democracy".
The shooting on the Champs Elysees took place at around 9pm local time when a vehicle stopped in front of a police van, Pierre Henry Brandet, the Interior Ministry spokesman, said.
A gunman opened fire on police, killing one officer and wounding three people before police shot and killed him.
The man "then ran away, managing to shoot and wound two other policemen".
Steve White, chairman of the Police Federation of England and Wales, said: "Once again the police family is in mourning and it serves to underline how courageous officers are putting their life on the line day in and day out to protect the public". Also wounded was a female tourist.More news: I don't feel extra joy at beating Chelsea - Mourinho
A still image from video footage shows Police investigators inspect the vehicle used by the attacker on the Champs-Elysees Avenue after two policemen were killed and another wounded in a shooting incident in Paris, France, on Thu., April 20, 2017.
A poll earlier this week found that more than half of French police officers plan to cast their vote for her at the election this weekend.
Security has been high in France leading up to the first round of hotly contested presidential elections Sunday.
Are you a New Zealander in Paris who witnessed the incident?
President Donald Trump responded to reports of a shooting Thursday in Paris by saying it looked like a terrorist attack.
The first round of presidential elections in France will be held on April 23, the second - on May 7.More news: White House pushes uncertain bid to revive health care bill
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