Analysts said last night's shooting, which the Islamic State (IS) group claimed as the work of one of its devotees, could shake up the race in a country scarred by a string of attacks that have claimed 239 lives since 2015.
Authorities had feared further bloodshed during the presidential race - a four-way contest between far-right leader Marine Le Pen, centrist Emmanuel Macron, conservative Francois Fillon and Communist-backed firebrand Jean-Luc Melenchon.
The violent scenes thrust security to the fore of campaigning after nine months of relative calm. Le Pen, Fillon and Macron cancelled their final rallies.
Le Pen moved quickly to present herself as the strongest defender against Islamist radicals.
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The 48-year-old leader of the anti-immigration National Front (FN) called for France to "immediately" take back control of its borders from the European Union and deport all foreigners on a terror watchlist.
Fillon and Macron also hastily convened televised briefings in which they vowed to protect the country.
"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 whom Fillon has portrayed as too inexperienced for the top job, said France was paying for the intelligence jobs cuts made when Fillon was prime minister between 2007 and 2012.
Describing yesterday's shooting as an attack on democracy, he urged voters: "Do not give in to fear."
A BVA poll conducted yesterday and today showed Le Pen and Macron tied on 23 per cent, ahead of Melenchon with 19.5 per cent and Fillon on 19 per cent.
Cheurfi drew up alongside a police van and shot an officer sitting at the wheel, sending shoppers and strollers on the ritzy Champs Elysees scattering for safety.
He was killed while trying to flee on foot. A German tourist was slightly wounded in the crossfire.
A statement by IS's propaganda agency Amaq issued shortly after the attack identified the assailant as "Abu Yussef the Belgian".
French authorities said a man sought in Belgium, who was suspected of having planned to travel to France yesterday, had handed himself in to police in the Belgian city of Antwerp.
Cheurfi was arrested in February on suspicion of plotting to kill police officers but released because of a lack of evidence.