The 54-year-old man was struck by a stray bullet while sitting at his home in Cayenne, the capital of French Guiana, on Friday.
Paramedics were unable to save him, local authorities said.
Violence erupted in Cayenne on Thursday night when gunshots were heard in the St Lucas district, a neighborhood with a reputation for urban violence.
Trash cans set on fire
Local media said police responding to reports of robberies and burning rubbish bins that night confronted about 20 youths who fired missiles at them. Three people were arrested and one was injured.
The following night, arson attacks were also reported in the communes of Macouria and Kourou.
Clashes were also reported on the Caribbean island of Martinique overnight Thursday and Friday, with most of the violence concentrated in the Ozanam neighborhood.
Police said the youths set up barricades with burning garbage cans to block the streets at the entrance to the city.
On the Indian Ocean island of Réunion, authorities have imposed a temporary ban on the sale of fuel after protesters set garbage bins on fire and threw rocks at police.
Three vehicles burned
The violence was worst in Le Port, a town on the island’s northwest coast, where rioters torched the Palace of Justice, torched three vehicles and vandalized a pharmacy.
About 150 officers were deployed to restore order. Three people were arrested.
France has 13 overseas territories, most of them remnants of the French empire.
Guyana, Réunion and Martinque are among five of the territories that have the same political and administrative status as the regions of mainland France.