He got out of the vehicle and fired an automatic weapon, killing one officer in the van, before shooting at others who were standing on the nearby pavement, injuring two before he was shot dead by police.
The attack brought back the recurrent campaign theme of France's fight against Islamic extremism, one of the mainstays of the anti-immigration platform of far-right leader Marine Le Pen and also, to a lesser extent, of Mr Fillon, a former prime minister.
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"Some haven't taken the full measure of the evil", 63- year-old Fillon said, promising an "iron-fisted" approach.
Macron, a 39-year-old moderate, is presenting himself as a guarantor of the European Union, promising reform and appealing to pro-Europe sentiment among the French electorate.
"We are suffering the consequences of a laxity that has continued for years", she said shortly before the shooting, promising to take a hard line against extremists and anyone suspected of being an Islamist.
Paris resident Daoud Kal, 29, said he was walking in the area near a metro station when he heard four to five shots. A foreign tourist was slightly wounded by shrapnel.
The terrorist group said it was behind the attack and named the gunman as Abu Yusuf al Beljiki, suggesting he was from Belgium. Cheurfi also had addresses of police stations written on bits of paper in his auto, he said. ISIS names a man it claims was involved in the attack. A second suspect in the attack, which also injured three people, has handed himself over to Belgian police after they alerted the French authorities of his possible involvement.
A French Interior Ministry spokesperson said he was an "individual known by the judiciary and police services - a unsafe individual".
France's Macron denies suggestions of impropriety
Also similar to what unfolded in the USA throughout 2016 is the media's cavalier dismissal of Le Pen as a serious candidate. Two other polls had Macron just ahead of Le Pen in the first round, and beating her comfortably in the second.
EU in focus as French presidential candidates face off
Under French election rules, Friday was due to be the final day of campaigning before Sunday's first round of voting. This attack will devastate Paris and it is one more unpredictable element in an already unpredictable campaign.
Security in Paris has been stepped up in recent days, but the presence of 50,000 police officers on the streets was not enough to prevent the latest assault, which a source tells CNN is being treated as an act of terror.
One police officer is dead and another hurt following a shooting in the French capital, police sources say. Police were questioning three people from his entourage.
A key question was how the attack might affect French voters, since campaigning is banned starting Friday at midnight.
In between, there have been a series of smaller attacks, often targeting security forces.
The warning was circulated more widely among French security services in the hour following the Champs Elysees attack.
Fillon, Le Pen and independent centrist Emmanuel Macron canceled planned campaign events after the shooting.
U.S. President Donald Trump waded into France's presidential election on Friday, tweeting that he expected the killing of a policeman in central Paris to have an impact on Sunday's vote.
"They are not living up to the spirit of the agreement, I can tell you that", Trump said of the Iranians on Thursday, though he did not mention any specific violations.
He said he and tourists fled to a shop.
France has lived under a state of emergency declared following a terrorist attack in November 2015 that left 130 dead.
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