The teenager, named as Nahel M, was shot at point-blank range as he drove off and crashed soon afterwards.
Paris police said they had contained "sporadic episodes" of fresh violence.
In Toulouse, protesters started a fire and threw stones at firefighters as they tried to put it out.
Demonstrators also clashed with police in the northern city of Lille.
French President Emmanuel Macron said the shooting of Nahel was "unforgivable".
The Alliance Police union called for them to be presumed innocent until found guilty, while the rival Unité SGP Police also spoke of political interventions that encouraged "anti-cop hatred".
Interior Minister Gérald Darmanin said he would be taking legal action against another group, France Police, after it published what he called an "unacceptable and abject" tweet seeking to justify the teenager's killing.
Prime Minister Élisabeth Borne also weighed in, saying the police intervention "manifestly did not conform to the rules".
Video of the incident on social media shows an officer pointing a gun at the driver of a car, before a gunshot is heard and the car then crashes to a stop.
The teenager died of bullet wounds in the chest, despite help from emergency services.
Nahel's mother Mounia, speaking in a social media video, said they had taken away her baby.
"He was still a child. He needed his mother," she said. "He kissed me goodbye in the morning and said, 'I love you mum'.
"An hour later, I was told that someone shot my son. What shall I do? He was my life. He was everything to me."
The officer accused of killing him, who said he had fired because he felt his life was in danger, is in custody on charges of voluntary manslaughter.
A series of protests followed the shooting on Tuesday night in Nanterre, just west of Paris. Some 31 people were arrested following the disorder.
