A man suspected of shooting dead three Kurds in Paris has been placed under formal investigation, while protests continue over the horrific attack. 

The 69-year-old man, whose name hasn't been disclosed, was arrested on Friday after two men and a woman were shot dead at a Kurdish cultural centre and nearby Kurdish cafe in Paris' busy central 10th district.

The killings stunned a community preparing to commemorate the 10th anniversary of the unresolved murder of three activists and prompted protests that led to clashes with police over the weekend.

The city prosecutor's office said on Monday that a man had been placed under formal investigation which under French law means there is serious or consistent evidence pointing to implication of a suspect in a crime.

The investigation carried out by a dedicated judge will look into charges of murder, attempted murder and unauthorised possession of a weapon, the prosecutor's office said in a statement.

It added that it suspected there was a racist motive behind the shootings.

Kurdish representatives have called for the shooting to be considered a terrorist attack. 

Many in the Kurdish community have expressed anger at the French security services, saying they had done too little to prevent the shooting.

There have been silent protests but demonstrations have also boiled over into violence and clashes with the police.

After a gathering on Friday afternoon that led to trouble with police, the Kurdish democratic council in France (CDK-F) organized a demonstration at Republic Square on Saturday.

Hundreds of Kurdish protestors, joined by politicians including the mayor of Paris' 10th district, waved flags and listened to tributes to the victims.

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"We are not being protected at all. In 10 years; six Kurdish activists have been killed in the heart of Paris in broad daylight," Berivan Firat, a spokesperson for the CDK-F, told BFM TV at the demonstration.

But frustrations again led to violence breaking out with the police.

On Monday several hundred people marched in the 10th, chanting "Our martyrs do not die" and demanding "truth and justice."

"We decided to come as soon as we heard about Friday's terrorist attack," one young woman said, declining to give her name for fear of reprisals.

The suspected killer - named as William M. by French media - is reportedly a gun enthusiast with a history of weapons offenses who had been released on bail earlier this month.