France's anti-terrorism prosecutor said Friday the gunman had a note with him defending the Islamic State group.
Le Pen's opponents say the jihadists want her to win, charging that the hardline anti-immigrant policies she wants to introduce would help militant groups like Islamic State to recruit.
The gunman was shot dead by police.
One police officer died after a gunman wielding a machine gun leapt out of a vehicle and opened fire on the Champs-Elysees, Paris's most famous boulevard, as candidates were engaging in their final TV debate.
The violent scenes thrust security to the fore of campaigning after nine months of relative calm. In a poll midweek, Macron appeared to have edged ahead of Le Pen.
"She's the strongest on borders and she's the strongest on what's been going on in France", Trump said in the Oval Office interview.
Some political commentators speculated the attack may give a boost to Marine Le Pen, the far right populist who says immigration threatens France's security and culture.
"This war against us is ceaseless and merciless", she said in a sternly-worded address, accusing the Socialist government of a "cowardly" response to the threat. "Some haven't taken the full measure of the evil", 63-year-old Fillon said, promising an "iron-fisted" approach. But Belgium's interior minister said the pseudonym did not belong to the attacker.
French President Francois Hollande convened a meeting of the country's defense council Friday.
The Champs Elysees shooting comes just days before the country's presidential election.
Communist-backed Melenchon, 65, was the only one of the four not to cancel his final campaign event on Friday.
One policeman was shot dead and two others were wounded in Thursday night's attack. The outcome of the election was being closely watched for signs that Europe is moving toward nationalist candidates like Le Pen.
He was killed while trying to flee on foot. A foreign tourist was slightly wounded by shrapnel.
Leftist candidate Jean-Luc Melenchon urged the French people to "remain cool-headed" and "to not subject ourselves to hate, vengeance and resentment".
Speaking during a televised debate around the time of Thursday's attack, Fillon said there was "no room for pursuing today or tomorrow an electoral campaign because first of all we have to demonstrate our solidarity with the police officers".
Cheurfi was known to anti-terror investigators, sources told AFP.
Three members of the gunman's family have been arrested for questioning.
For Sunday's vote, the government is mobilizing more than 50,000 police and gendarmes to protect the 70,000 polling stations, with an additional 7,000 soldiers also on patrol.
Almost a quarter of voters are still undecided, and surveys showed until now the French to be more concerned about jobs and the economy than terrorism.
"The likelihood of more terror attacks in the French presidential elections is very high", he said.
Adelaide Zulfikarpasic of BVA pollsters said: "If it were to benefit someone that would clearly be Marine Le Pen who has dominated this issue throughout the campaign, or Francois Fillon". "The people of France will not take much more of this".
Shop owners and restaurant managers shepherded their customers to backrooms and basements when the shooting began on the Champs-Elysees.
"We sympathise with the French people and support the French authorities in solidarity with dealing with this", he said. "But people were calm", said Lebanese tourist Zeina Bitar, 45, who was shopping with her children nearby.
France has been under a state of emergency since November 2015.
14 Jul 2016 - A huge lorry mows down a crowd of people on the Nice beachfront during Bastille Day celebrations, killing 86.