The French government has urged cities hosting Euro 2016 matches to ban alcohol near venues and fan zones.
It follows three days of clashes between fans and police in Marseille.
Uefa is investigating after Russia supporters appeared to rush at England fans in the stadium after their draw on Saturday. It has threatened to ban both teams if there is further fan violence.
The UK government has offered to send extra British police ahead of England’s next match in Lens on Thursday.
French Interior Minister Bernard Cazeneuve 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 ban will include public areas, as well as shops and off-licences, Mr Cazeneuve said.
Senior local officials can also ban bars and cafes from serving drinks on their terraces in containers that can be used as missiles.
“The events which took place in Marseille… are unacceptable. Unacceptable for the authorities, unacceptable for society, unacceptable for football lovers,” Mr Cazeneuve said.
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.
Lens has already banned alcohol from being sold and fans without tickets for the match or fan zone have been told not to travel.
Uefa, European football’s governing body, said it had begun disciplinary proceedings against Russia – but not England – after “totally unacceptable” scenes at the England-Russia game which ended 1-1.
Charges against Russia are for crowd disturbances, racist behaviour, and setting off fireworks, Uefa said.
There were issues with segregation of fans, the body admitted, promising security would be “strengthened”.
Witnesses said trouble began in the stadium 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.
Sanctions against Russia will be decided at a disciplinary meeting on Tuesday, Uefa said.
BBC sports editor Dan Roan said as hosts of the 2018 World Cup, the country was under intense scrutiny.
Russian and English supporters as well as French locals also clashed in pitched battles for three days in Marseille ahead of their teams’ first-round encounter.
As many as 20 England fans were injured, with a number taken to hospital, and at least one Briton is understood to be in a critical condition.
Uefa said it had not taken any action against the English FA, because skirmishes involving England fans before kick-off fell outside its remit.
FA chief executive Martin Glenn said a letter from Uefa about fans’ behaviour, was being treated with the “utmost seriousness”.
“We understand the potential implications of our supporters’ actions and wholly accept that every effort needs to be made by the FA to positively urge them to act in a responsible and respectful way,” he said in a statement.
“Violent scenes like those witnessed over the weekend in Marseille have no place in football, nor society as a whole.”