An off-duty British policeman has received minor injuries while travelling to watch the England match.
The attack, which took place while he was walking to the Donbass Arena, is believed to be an isolated incident.
Pc David Heasman, 45, from Norfolk Police, said he was punched and kicked by a group of four men who he said claimed to be "Russian mafia", and received a cut to the ear but did not require hospital treatment.
Pc Heasman, a married father of two, said he was walking to the stadium when a group of men ran up behind him and his fellow England supporters shouting "we are the Russian mafia".
"I turned round and one of them punched me in the face," he said. "I fell to the ground and I felt two kicks to the head. It hurt. I feel upset because it's been a nice atmosphere until now. The police are out in force but they're not there when you need them. They're just standing on show on street corners."
A handful of British police officers were on patrol around the bar in the city centre, while their Ukrainian counterparts kept watch from across the road as flags of St George were hung from a marquee.
Eighteen British officers have been deployed in Ukraine and six in Poland - led by the Association of Chief Police Officers - to help up to 8,000 local armed police deal with fans at games.
Some supporters proved their dedication by enduring a sweltering 13-hour overnight train journey from the capital Kiev. Others enjoyed more comfort, with hundreds arriving in the industrial city of Donetsk by charter flights which left London earlier today.
The number of travelling England fans will be the lowest at a tournament for many years, with around 3,000 tickets sold through the official supporters' club for tonight's game.
But the lack of demand meant that fans in Donetsk were able to buy spare tickets from other supporters without an inflated price.
Dex Marshall, 52, from Uckfield, East Sussex, said: "No one is paying more than face value. There are plenty of England fans with extra tickets that they won't be able to get rid of. I know people who haven't come because their wives and partners were worried by the racism and hooligan stories."
Joss Orpin, 23, was among a group from Leicester who arrived in Donetsk at 8am after a marathon train ride from Kiev.
He said: "It was really hot and they didn't have any windows in the cabins. They said there was air conditioning but it didn't work."
France went into the match as strong favourites after a 21-game unbeaten run, while England are missing Wayne Rooney through suspension and have suffered a number of injuries to key players.
The weather could also be a factor, with experts predicting maximum temperatures of 30C (86F).
Assistant Chief Constable Andy Holt, who is leading the British police contingent in Donetsk, said there have been no reports of disorder by England fans, but some may suffer from excessive alcohol intake in the "red hot" conditions.
He said: "There's been no problems. There are a few at the campsite that I don't think are going to make it to the game because of drink."
He said the number of England shirts being worn by people of other nations - especially Russian - presented a challenge to his officers.
"What I don't want to do is have England fans mislabelled, misidentified because it's some other nationality wearing an England shirt," he added. "You can imagine that we will be very careful to ensure that if there is any sort of problem we identify the provenance of who we're dealing with."
