Some 150 Russians were behind much of the violence in Marseille ahead of the Euro 2016 match between England and Russia, according to reports from French prosecutors.
It also opened disciplinary proceedings against the Russian Football Union for alleged crowd disturbances, racist behaviour and the setting off of fireworks by its fans during the match.
England fans were seen fleeing the stands shortly after the final whistle was blown as balaclava-clad thugs punched through a line of stewards before attacking bystanders.
The incident raised serious questions about French security at a time when the country is on high alert after November's terrorist attacks on Paris.
The scenes from Marseille were described by the Football Association as "terrible" as it called on the local authorities to deal with the perpetrators swiftly.
The fights began hours before kick off at the Old Port area and led to several Brits being seriously hurt along with claims that gangs of Russian fans were hunting England supporters.
According to Marseille prosecutor Brice Robin, 20 people have been arrested and 10 people, including six Britons, face an immediate trial, the BBC reported. A 16-year-old Briton is said to be among those arrested and charged with throwing bottles.
Robin said only two Russians had been arrested. He added that they were "well trained" and "well prepared".
Robin told a news conference: "These people [the Russians] were well prepared for ultra-rapid, ultra-violent action."
This was what made it difficult to arrest them, the prosecutor said.
Robin said the Russian hooligans were not thought to be "professional" but he said they were "extreme".
About 35 people have reportedly been injured in clashes between fans, including four whose conditions were said to be serious.
News of the arrests comes as the French government urged cities hosting Euro 2016 matches to ban alcohol near venues and fan zones. The ban was to include public areas, as well as shops and off-licences.
French Interior Minister Bernard Cazeneuve is quoted by the BBC as saying: "I have asked for all necessary measures to be taken to prohibit the sale, consumption and transport of alcoholic drinks in sensitive areas on match days and the day before, and on days when fan zones are open."
Senior local officials can also ban bars and cafes from serving drinks on their terraces in containers that can be used as missiles.
Cazeneuve added: "The events which took place in Marseille... are unacceptable. Unacceptable for the authorities, unacceptable for society, unacceptable for football lovers."
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ASSOCIATED PRESS
A man walks toward teargas fired by police, following scuffles in Marseille, France, early Friday, June 10, 2016. Trouble flared outside an Irish pub in the Old Port of the southern city just before midnight Thursday, apparently between English fans drinking there and some local people. Marseille is hosting a European Championship soccer match between England and Russia on Saturday. (AP Photo/Darko Bandic)
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Police patrols on a street following scuffles in Marseille, France, early Friday, June 10, 2016. Trouble flared outside an Irish pub in the Old Port of the southern city just before midnight Thursday, apparently between English fans drinking there and some local people. Marseille is hosting a European Championship soccer match between England and Russia on Saturday. (AP Photo/Darko Bandic)
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A plain clothed French police officer (R) talks to an England fan as others shout and chant outside a bar
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MARSEILLE, FRANCE - JUNE 09: Police officers look on as England fans shout and chant outside a bar ahead of the England v Russia game on Saturday, on June 9, 2016 in Marseille, France. Football fans from around Europe have descended on France for the UEFA Euro 2016 football tournament. (Photo by Carl Court/Getty Images)
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A tear gas canister discharged by police to disperse England football fans.
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The Queen Victoria pub where police dispersed England football fans.
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A member of staff cleans up at The Queen Victoria pub where police dispersed England football fans after an apparent clash with locals in the Old Port district of Marseille ahead of the first game in Euro 2016.
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A fan using a wheelchair is lifted by his fellows, in Marseille, France, Friday, June 10, 2016.
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An England supporter is thrown into the air for fun as they gather and drink in downtown Marseille, France, Friday, June 10, 2016.
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English football fans as they gather in the old town area of Marseille ahead of the first game in Euro 2016.
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A woman watches as football fans (nationality unknown) set upon a man wearing an orange top, prior to throwing him in the habour, where he managed to swim to shore, in the old town area of Marseille.
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French police officers watch chanting English football fans in the old town area of Marseille.
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A man is apprehended by French police in downtown Marseille.
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England supporters taunt a line of French riot police officers in downtown Marseille.
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Two English football fans throw bottles (centre) towards French as two French plain clothes officers raise their asps (far right, green top and black top) as French and English football fans gather in the old town area of Marseille.
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French riot police form a line to confront England supporters.
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A man is apprehended by French police.
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French police officers run towards football fans in the old town area of Marseille ahead of the first game in Euro 2016.
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English football fans as they gather in the old town area of Marseille.
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A French woman (in pink) throws a beer bottle towards English football fans.
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A French woman is led away by police after throwing a beer bottle towards English fans.
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French police officers watch chanting English football fans.
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English football fans gesture towards French fans.
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French police dog handlers walk past football fans.
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England football fans shout as they clash with police.
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England supporters take evasive action after French police fired tear gas at them in downtown Marseille.
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A French police officer holds a baton gun following clashes with English football fans.
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England supporters were forced to jump over a fence to escape Russian thugs
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Fans had to flee as they came under attack in the stands
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Tempers flared between both sides, witch many scenes of unprovoked violence
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Stewards later managed to intervene in some brawls
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Some of the agitators wore black masks to conceal their identities