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.
However, Kevin Miles of the Football Supporters’ Federation, which represents fans in England and Wales, said a ban would not work.
“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,” he said.
“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.”
On Sunday, Uefa, European football’s governing body, announced 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.