Schweinsteiger has been in doubt to appear in the tournament due to injury, but came on to prove he is back in fitness by marking his first appearance since March in style.
In imposing the alcohol ban, 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.”
Also on Sunday, UEFA warned England and Russia they could be sanctioned because of the behaviour of their supporters.
UEFA said both nations could face expulsion from the tournament if there are any further incidents.