The violence on Monday was believed to be a local reaction to three days of violence by Chechen gangs in Dijon.
Calm has been restored to the streets of a Dijon suburb after four days of unrest.
On Friday a large group of Chechens began clashing with the North African community looking to settle scores after the beating of a teenage Chechen boy.
Some media reports suggest members of the Chechen community travelled across France, Belgium and Germany to reach Dijon.
Dozens of men armed with guns and crowbars wreaked havoc on the low-income district of Grésilles, burning cars and rubbish bins and destroying CCTV cameras.
In one incident, a team of journalists from public broadcaster France 3 was attacked by men who stoned their vehicle.
France’s Junior interior Minister Laurent Nunez toured the area on Tuesday and promised an "extremely strong response" with more than 150 police and gendarmes mobilised to reassure residents.
Marine Le Pen, the leader of France’s far-right National Rally party, also paid a visit and blamed lax immigration policies for the unrest.
"This is a situation of unprecedented gravity. It goes beyond a news story and should be seen as a warning to our nation," Le Pen said.
One of the men who took part in the violence confirmed to a local newspaper that an attack on a community centre on Friday was a revenge attack after a local drug dealer assaulted a 16-year-old Chechen youth.
On Saturday night, around 50 Chechen men returned to the Grésilles district, where a local manager of a pizza restaurant was shot. On Sunday, as many as 200 men took to the streets in the district.
Bernard Schmeltz, the region's prefect, said that the disturbances on Monday night were believed to be revenge attacks for the violence of the previous three evenings.
Schmeltz and the local authorities have come under fire for a lack of intervention into the violence over the weekend, but he said that "supervising and surrounding" the gangs was "the only practicable strategy."
Eric Mathais, Dijon's prosecutor, said that at least six people had been wounded over the past three days, and that an investigation had been opened into the violence.