Security has been especially high since Tuesday, when police said they thwarted a terror attack by arresting two men.
The Champs Elysées has been closed as the authorities investigate.
The police union said one of the officers was killed, while the other officer was seriously injured. The shooter, whose identity is still unknown, has reportedly been shot dead.
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The Paris prosecutor's office said counterterrorism investigators are involved in the probe of Thursday's attack.
Conservative presidential contender Francois Fillon said he was cancelling his planned campaign stops on Friday and far-right candidate Marine Le Pen took to Twitter to offer her sympathy for law enforcement officers "once again targeted".
Emergency vehicles blocked the wide avenue that cuts across central Paris between the Arc de Triomphe and the Tuileries Gardens, normally packed with cars and tourists.
The gunfire sent scores of tourists fleeing into side streets. "Some were crying. There were tens, maybe even hundreds of them".
France has lived under a state of emergency since 2015 and has suffered a spate of Islamist militant attacks that have killed more than 230 people in the past two years.
He says police are securing the area but there is "no other police operation underway" in the popular area.
Thursday night's attacker got out of a auto that pulled up next to a police van on the Champs Elysees and opened fired on officers inside and standing by the vehicle, Interior Ministry spokesman Pierre-Henry Brandet told reporters at a police barrier on the avenue. He said it is too early to know if the gunman had an accomplice.
Speaking in Washington during a news conference with Italian Prime Minister Paolo Gentiloni, U.S. President Donald Trump said the shooting "looks like another terrorist attack" and sent condolences to France.
The shooting comes two days after the arrest of two men in southern Marseille with weapons and explosives who were suspected of preparing an attack to disrupt the first-round of the presidential election on Sunday. It identified the attacker as Abu Yussuf al-Baljiki, suggesting he's from Belgium - details not confirmed by the French authorities.
And in March, a 39-year-old man was killed at Paris's Orly airport after attacking a soldier.
None of the candidates immediately commented.