As well as the death of Mr Jugele, two other police officers and a German tourist were injured when Cheurfi opened fire. A foreign tourist was slightly wounded by shrapnel.
Officials told the Associated Press the gunman was detained in February for threatening police, but was let go.
Authorities said Cheurfi had a long criminal record and an apparent hatred of the forces of law and order and had been jailed for attempted homicide after attacking two police officers in 2001. French President Francois Hollande classified the incident as a terrorist attack.
The shooting mirrored recent attacks on French soldiers at prominent locations around Paris: at the Louvre museum in February and at Paris' Orly airport last month. But his statement on Twitter - "The people of France will not take much more of this".
"Another terrorist attack in Paris".
French officials on Friday reviewed the government's heightened security plans for the presidential election. France's unemployment rate is about 10 percent, more than twice as high as that of its neighbor Germany, and the state of the economy is a constant worry.
And despite complimentary comments about some of her policies, White House spokesman Sean Spicer firmly denied that Trump had a preferred candidate in the race.
The two top contenders Sunday will advance to the runoff on May 7.
Le Pen took the second place in the poll with 23 per cent, up 1 point.
ISIS has previously assigned war names to militants who carried out attacks in Paris and Brussels that were coordinated with commanders in Syria. She promised to beat "Islamic terrorism".
One of them, Marine Le Pen, the far-Right candidate, has issued grim warnings that a declining France is losing its identity, echoing Trump's themes during the American presidential race past year.More news: North Korea attempts but fails to launch missile - South Korea
Socialist Prime Minister Bernard Cazeneuve accused Le Pen of attempting to exploit the killing, "as she does after every tragedy". "And whoever is the toughest at the borders will do well in the election". Speaking on Friday, Belgian Interior Minister Jan Jambon denied that Cheurfi had Belgian citizenship, and insisted that Abu Yousif al-Belgiki "is certainly not the guy who committed the crime yesterday". He formed a new centrist party and entered the presidential race as a maverick outsider.
Macron "now has good chances to come first in the first round and is therefore unlikely to be eliminated", Odoxa's Gael Sliman said in a note accompanying the poll.
"It puts internal security on the top of the agenda and on the top of people's consciousness so I would think that this is definitely going to affect people's decisions on Sunday", she said.
Police authorities called on the public to avoid the area.
However, conservative former Prime Minister Francois Fillon, whose campaign was initially derailed by corruption allegations that his wife was paid as his parliamentary aide, appeared to be closing the gap, as was far-leftist, Jean-Luc Melenchon.
Surveys suggest that almost a quarter of voters are still undecided and that until now the French have been more concerned about jobs and the economy than terrorism.
Fillon also spoke about the latest attack.
France, the world's sixth-largest economy and a key player in Europe, has been under a state of emergency since the November 2015 terror attacks in Paris. "This must be the priority", he said.
France has been under a state of emergency for almost a year and a half. Hai Do was the editor.
"We heard the shots and people were running in every direction".