Supporters of the bans say the garment - which some Muslim women wear to meet with Islamic requirements to dress modestly in public - collides with French secular principles.
But anti-racism campaigners saying that banning women from wearing it amounts to discrimination.
Burkinis were the apparent cause of the brawl on a beach near Sisco on Sunday.
The village's mayor said that the incident started when a tourist took a photo of some young women wearing burkinis.
"And the Maghrebins (North Africans) didn't want to have their photos taken. It was quite a trivial matter to begin with," Vivoni said.
A hundred police officers were mobilised to break up the fight, which lasted for several hours.
A series of incidents in Corsica have raised tensions in recent months between local Muslims and their neighbours.
Last Christmas Day a mob ransacked a Muslim prayer hall and set fire to copies of the Koran in the Corsican capital Ajaccio after an assault on firefighters that was blamed on youths of Arab origin.
In July Corsican politicians called on the French state to close down radical mosques on the island, after an underground separatist movement issued a threat against Islamic extremists.
A splinter group of the nationalist Corsican National Liberation Front (FLNC) warned Islamists that any attack on the island would trigger "a determined response, without any qualms".
ABOUT BURQAS - WHERE THEY ARE BANNED
Burqa: full body covering with mesh over the eyes
Niqab: full body covering with a slit for the eyes
Full burqa and niqab ban
France, since 2004
Belgium, since 2011
Chad, since 2015
Cameroon, in five provinces, since 2015
Diffa, Niger, since 2015
Brazaville, Congo, since 2015
Tessin, Switzerland, since 2016
Partial burqa and niqab ban
The Netherlands: women cannot have their faces covered in schools, hospital and on public transport
The Italian town of Novara: women were told to stop wearing a full veil in 2010, but there is no established fines system
Parts of Catalonia, Spain: The country's Supreme Court ruled against a ban in some areas in 2013, however those areas which brought their cases to the European Court of Human Rights (ECHR) have continued with the ban - supported by an ECHR ruling in their favour in 2014
Turkey: a full ban was abandoned in 2013. Now, women are only barred if they work in the judiciary, military and police