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The clashes in the stadium on Saturday followed England's 1-1 Euro 2016 draw with Russia, after Russia fans appeared to rush at England supporters.
Marseille prosecutor Brice Robin told a news conference: "There were 150 Russian supporters who in reality were hooligans. These people were well prepared for ultra-rapid, ultra-violent action. These are extremely well-trained people."
This was what made it difficult to arrest them, the prosecutor said, adding that he did not think the Russian hooligans were "professional" but that they "were extreme".
The first England fan to appear in court in Marseille on Monday was 20-year-old Alexander Booth, from Huddersfield, West Yorkshire.
He was sentenced to two months for throwing a plastic bottle at police.
Reacting to the sentence, Booth's father Chris, who was later seen in tears, said he would "fight it".
The second England fan was Ian Hepworth, 41, a psychiatric from Sheffield, who was sentenced to three months for throwing a bottle at police and then walking forward to pick up a second bottle.
Both were banned from France for two years each.
In other developments:
In addition to six Britons, another four - three French and an Austrian - are due to appear in court imminently
A 16-year-old Briton was among those arrested and charged with throwing bottles
Two Russian nationals were being expelled from the country, French prosecutors said
Seven England fans are still in hospital, Mrs May told the Commons
During the press conference, Mr Robin said officers were looking at pictures with foreign colleagues - Russian and English football spotters - to try to identify those involved in the disorder.
And British Assistant Chief Constable Mark Roberts, the National Police Chiefs' Council lead for football policing, appealed for fans with their own camera phone footage to contact crime-fighting charity Crimestoppers.
Witnesses said trouble began in the stadium on Saturday after flares were let off by Russian fans near the end of the game. Some then climbed across barriers designed to keep rival fans apart.
A number of Russia supporters appeared to kick and punch fleeing England fans, who were forced to clamber over fencing to escape.
Uefa has been investigating and has threatened to ban both teams if there is further violence.
It also opened disciplinary proceedings against the Russian Football Union for alleged crowd disturbances, racist behaviour and the setting off of fireworks.
There were 12,000 Russian fans in Marseille who travelled to the city by train, according to French prosecutors.
Sanctions against Russia will be decided at a disciplinary meeting on Tuesday, Uefa said.
Russia's sports minister, Vitaly Mutko, said Uefa had "done the right thing" to start a disciplinary case against the Russian Football Union, R-Sport news agency reported.
But Russian MP Igor Lebedev criticised French police and called on Russian football fans to "keep up the good work".
Russia's next match against Slovakia will take place in Lille on Wednesday - the day before England's match against Wales, just 24 miles away in Lens.