According to widespread reports, tear gas was used as French police attempted to defuse the trouble, which took place late on Thursday night.
UEFA has released a statement expressing their regret at the incident, but stressed their confidence in local authorities to maintain order during the tournament.
The statement read: "UEFA regrets the skirmishes that occurred in Marseille.
"We are confident that the safety of travelling fans will be ensured by the local authorities which are responsible for order in the city.
"We make an appeal to all fans to behave respectfully throughout the tournament."
England are in Group B for the competition along with Russia, Slovakia and Wales.