Police in central Paris opened fire on a car that was hurtling towards them, killing two people inside, a police source told AFP, just hours after French President Emmanuel Macron won a second term.

The vehicle was driving on Paris's oldest standing bridge, the Pont Neuf, shortly after midnight when it refused to stop at a police checkpoint. As it sped towards the officers, they opened fire, according to the same police source.

Two of the vehicle's occupants were killed and a third was injured, said the source.

A large police presence descended upon the scene in the heart of the capital, where white sheets covered the bodies and a Volkswagen sedan could be seen bisecting traffic lanes, according to AFP journalists and photographs.

Less than two kilometres (1.2 miles) away, French President Emmanuel Macron was celebrating his victory over far-right rival Marine Le Pen with a crowd of supporters on the Champ de Mars park.

His win closed out a tense contest that saw the French far right come the closest it ever has to winning the presidency.

No link has been established between the bridge incident and the election night events.

An Egyptian tourist, who gave his name as El Sammak, said he was near the incident on the terrace of the White Horse Hotel overlooking the Seine when he heard the shooting.

"I heard four bullets (being fired)," he told AFP. "When I looked, I saw a man running 10 or 15 metres. Then he collapsed. Apparently, he was not the driver but a passenger."

An investigation has been launched for "attempted voluntary manslaughter on persons in charge of public authority".

The Paris public prosecutor, Laure Beccuau, arrived around 1:30 am (2330 GMT).

France's police oversight body, the General Inspectorate of the National Police, is also expected to be deployed, as is typical following an officer's use of a firearm.