The updated warning comes after the violence surrounding the England vs Russia match in Marseille at the weekend.
Highly trained and organised Russian ‘ultras’ were blamed for much of the violence in the southern port city which left dozens of people hurt, some of them seriously.
“There were scenes of significant violent disorder affecting fans in Marseille from 9-11 June,” the FCO said.
“Fans travelling to the Lens/Lille area for the England versus Wales match on 16 June should be aware that the match between Russia and Slovakia will take place in Lille on 15 June and large numbers of fans are expected to be in the city.
In pictures: Euro 2016 violence in Marseille
An England fan is detained by French security personnel in the city of Marseille, southern France, on June 11, 2016
English supporters at the Old Port of Marseille, France, 11 June 2016
An England fan kicks away a tear gas canister after tear gas was released by French police in the city of Marseille, southern France, on June 11, 2016
An England fan in clashes with police in Marseille on June 11, 2016
French police officers charge England fans in Marseille
England football fans shout as they clash with police in Marseille
England fans throw bottles at police in Marseille
A tear gas canister explodes under a football fan as England fans clash with police in Marseille
French riot police used tear gas to disperse England fans on a second day of clashes
French police monitor England fans in Marseille
England fans grouped at O’Malley’s pub in Marseilles on Thursday night
Trouble flared outside an Irish pub in the Old Port of the southern city of Marseilles just before midnight Thursday
“Fans are advised to be cautious and those without tickets for the match should avoid Lille and Lens during this period.”
The towns of Lille and Lens are less than 25 miles apart.
A 24 hour alcohol ban has been imposed in Lens for the England vs Wales match, an action the French government has encouraged nationwide.
However, ticketless supporters had previously been told by British police to travel to fan zones in Lille, where many Russian fans are expected around the same time. Lille also had no alcohol ban planned.
But on Sunday, French Interior Minister Bernard Cazeneuve asked the cities hosting Euro 2016 fixtures to ban the sale and consumption of alcohol in zones where the risk of confrontation was most acute.
He said: “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.”
“The events which took place in Marseille are unacceptable,” Mr Cazeneuve added. “Unacceptable for the authorities, unacceptable for society, unacceptable for football lovers.”
“We witnessed violence between fans, caused by alcoholic hordes who have engaged in unacceptable abuses.”
However, fans have disputed that alcohol was the cause of the violence. Chief Executive of the Football Supporters Federation, Kevin Miles, told the BBC: “What we’ve seen there is groups of locals getting together and Russian hooligans getting together with the deliberate intent of attacking football fans, English fans primarily, while they’ve been enjoying their drinking and their eating at places.”
“And I’ve been personally the victim of that. But the crucial thing is here, the Russians and the locals here who have been attacking football fans have been stone cold sober. They don’t drink, they are consciously focused, they train for six months, preparing for acts of hooliganism and violence like this. They’re not drunk, that’s not what’s caused the violence here.”