Ian Hepworth, a 41-year-old psychiatric nurse was sentenced to three months in prison. Alexander Booth, a 20-year-old chef, received a two-month term. Both were banned from France for two years.
They were the first of 10 men to be tried for their part in the mass fighting in the southern French city at the weekend, the worst violence to hit a major football tournament since the 1998 World Cup which was also held in France.
Hepworth admitted throwing a beer bottle at police at 1.00 am on Sunday, following England's match with Russia on Saturday.
"My job is helping people. I did something stupid," he said through a court translator.
Hepworth, wearing a blue shirt and with a shaven head, said he had had no intention of hitting police with the bottle.
"I wanted to impress my new French friends," he told the court.
Before the incident, he had attended the match at the Stade Velodrome alone.
Booth, who was wearing an England team t-shirt, admitted throwing a plastic beer cup and making an offensive gesture at police in the Vieux-Port district of Marseille on Saturday evening.
Prosecutor Andre Ribes said police had reported that Booth had thrown a glass bottle and had aimed for their legs under their shields.
Booth told the magistrate he was "hard-working" and insisted: "This is not like me."
"I apologise to the people and the police of Marseille... I was at the wrong place at the wrong time," he told the court.
Another eight supporters arrested in the violence are to be tried on Monday -- four more Britons, an Austrian and three French.
Marseille's prosecutor said Monday that 150 "extremely well-trained" Russian hooligans had evaded arrest in the violence, the worst to hit a major football tournament since the 1998 World Cup, also held in France.
An English man in his fifties who was seriously injured in the violence is in a critical but stable condition in hospital, officials said.
UEFA have warned Russia and England they could be disqualified from the tournament if their fans are involved in any further violence.
England captain Wayne Rooney and manager Roy Hodgson on Monday pleaded with the country's fans to behave.
"I'm appealing to you to stay out of trouble," Hodgson said in a video message. "We really desperately want to stay in the competition."
Rooney told fans: "Be safe, be sensible and continue with your great support for the players."
