The Islamic State extremist group quickly claimed responsibility for Thursday night’s attack, just three days before a tense presidential election.
Security has already has been a dominant theme in the campaign and the violence on the city’s iconic avenue threatened to have a bearing on voters’ decisions.
Candidates cancelled or rescheduled final campaign events ahead of Sunday’s first-round vote.
Investigators searched a home early on Friday in an eastern suburb of Paris believed to be linked to the shooting.
A police document identifies the address searched in the town of Chelles as the family home of 39-year-old Karim Cheurfi, who has a criminal record.
Police tape surrounded the quiet, middle-class area and neighbours expressed surprise at the searches.
Archive reports by French newspaper Le Parisien say Cheurfi was convicted of attacking a police officer in 2001.
Authorities are trying to determine whether “one or more people” might have helped the attacker, Interior Ministry spokesman Pierre-Henry Brandet said at the scene of the shooting.
One police officer was killed and two colleagues seriously wounded when the attacker emerged from a car and used an automatic weapon to shoot at officers outside a Marks & Spencer store at the centre of the Champs-Elysees, anti-terrorism prosecutor Francois Molins said.
The gunman was shot dead by other officers.
A female foreign tourist also was wounded, Mr Molins said.
The IS group’s claim of responsibility just a few hours after the attack came unusually swiftly for the extremist group, which has been losing territory in Iraq and Syria.
In a statement from its Amaq news agency, the group gave a pseudonym for the gunman, Abu Yusuf al-Beljiki, indicating he was Belgian or had lived in Belgium.
Belgian authorities said they had no information about the suspect.
IS described the shootings as an attack “in the heart of Paris.”
The attacker had been flagged as an extremist, according to two police sources.
Mr Brandet said officers were “deliberately” targeted, as has happened repeatedly to French security forces in recent years, including in the run-up to the 2012 election.
Police and soldiers sealed off the area, ordering tourists back into their hotels and blocking people from approaching the scene.
Emergency vehicles blocked the wide Champs-Elysees, an avenue lined with boutiques and normally packed with cars and tourists that cuts across central Paris between the Arc de Triomphe and the Tuileries Gardens. Tube stations were closed off.
The gunfire sent scores of tourists fleeing into side streets.
“They were running, running,” said 55-year-old Badi Ftaiti, who lives in the area.
“Some were crying. There were tens, maybe even hundreds of them.”
President Francois Hollande said he was convinced the circumstances of the attack in a country pointed to a terrorist act.
Mr Hollande held an emergency meeting with the prime minister on Thursday night and was due to convene a meeting of the defence council on Friday morning.
The incident recalled two recent attacks on soldiers providing security at prominent locations around Paris - one at the Louvre museum in February and one at Orly airport last month.
Speaking in Washington during a news conference with Italian prime minister Paolo Gentiloni, US president Donald Trump said the shooting “looks like another terrorist attack” and sent condolences to France.
A French television station hosting an event with the 11 candidates running for president briefly interrupted its broadcast to report the shootings.
Conservative contender Francois Fillon, who has campaigned against “Islamic totalitarianism”, said he was cancelling his planned campaign stops on Friday.
Far-right candidate Marine Le Pen, who campaigns against immigration and Islamic fundamentalism, took to Twitter to offer her sympathy for law enforcement officers “once again targeted”. She cancelled a minor campaign stop, but scheduled another.
Centrist candidate Emmanuel Macron offered his thoughts to the family of the dead officer and Socialist Benoit Hamon tweeted his “full support” to police against terrorism.
The two top finishers in Sunday’s election will advance to a run-off on May 7.