The 32-year-old victim was killed early Friday evening in a park on a notorious housing estate as mothers and small children watched.
Horrified witnesses of the attack in Pau, southern France, said the gang of a dozen teenagers were all aged up to 16 and 17.
The gang repeatedly kicked and punched the victim, who was also beaten with a plastic chair leg and a piece of wood.
French media have called the attack a “terrifying lynching”.
The murdered man has not been named but he is said to be a French national from Burkina Faso, who had moved to Pau from Paris in recent years.
He is believed to have been known to police for aggravated robbery and drug trafficking, but one official said: “No link has been established between the man’s past and the events of Friday evening in Pau.”
According to French media, the gang was made up of teenagers who lived on the Saragosse estate.
Newspaper Sud Ouest quoted a young mother who saw the attack as saying: “There were 12 on him, then he fell to the ground. Four of them carried on beating him and there was one who finished him off.”
Another witness, who was picnicking on the grass with children when the attack started, said: “I’m still in shock – I cannot believe what I saw.”
She added: “There were a dozen on him, beating him. It was unbelievable. There was nothing we could do other than alert the emergency services.
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“My daughter said to me ‘mum there was a fight and the man has gone to heaven’. At her age, she’s never seen this kind of thing. If I could, I would move home.”
The three arrests were prompted by the discovery of DNA on one of the objects used to beat the man.