The shooting, in which the assailant was also killed, took place on the Champs-Elysees shopping boulevard just days ahead of Frances presidential election.
A witness told Reuters that a man got out of a car at the scene and began shooting with a machine gun. A police source also said more shots had been fired at another location near the scene.
A French interior ministry spokesman said it was too early to say what the motive of the attack was, but that it was clear the police officers had been deliberately targeted.
The French prosecutors office said the counter-terrorism office had opened an inquiry.
Three police sources said, however, that the shooting could have been an attempt at an armed robbery.
"I came out of the Sephora shop and I was walking along the pavement where an Audi 80 was parked. A man got out and opened fire with a kalashnikov on a policeman," witness Chelloug, a kitchen assistant, told Reuters.
"The policeman fell down. I heard six shots, I was afraid. I have a two year-old girl and I thought I was going to die... He shot straight at the police officer."
Police authorities called on the public to avoid the area.
TV footage showed the Arc de Triomphe monument and top half of the Champs Elysees packed with police vans, lights flashing and heavily armed police shutting the area down after what was described by one journalist as a major exchange of fire near a Marks and Spencers store.
The incident came as French voters prepared go to the polls on Sunday in the most tightly-contested presidential election in living memory.
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.
Earlier this week, two men were arrested in Marseille whom police said had been planning an attack ahead of the election.
A machine gun, two hand guns and three kilos of TATP explosive were among the weapons found at a flat in the southern city along with jihadist propaganda materials according to the Paris prosecutor.