Officers from the UK Football Policing Unit (UKFPU) are hoping to identify the men following the clashes ahead of England’s Euro 2016 game against Russia on Saturday June 11.
Police also appealed for people to hand over any photos or video of the fighting, which left 14 England football fans in hospital.
Among them was Andrew Bache, 51, who suffered a cardiac arrest, extensive brain injuries and a lung infection after being set upon by Russians armed with iron bars.
There is no suggestion from authorities he was suspected of being involved in the disorder.
A group of 150 ‘hyper rapid, hyper violent’ Russian hooligans attacked Three Lions supporters in the French port city, throwing chairs and beer bottles in violent scenes the National Police Chiefs’ Council (NPCC) said were ‘on a scale we haven’t seen for many years’.
Two England fans are still in hospital with serious injuries, including Andrew Bache, 51, from Portsmouth and Stewart Gray, 47, from Leicester, who was found injured near the Rue Forte Notre Dame area at 4pm.
Police said Mr Gray, who recently opened his eyes after being in a coma, was wearing a blue t-shirt and was part of a group of fans who had gathered in the city centre at around 2.30pm. Officers have no footage to show how he came to be injured.
Detective Superintendent Andy Barnes, who is leading the UKFPU investigation, said: “Please come forward if you have any information, photos or video of what happened in Marseille.
“We particularly need footage to help us understand how Stewart Gray became so badly injured. We are aware that there were people in the apartment above the incident who we would like to speak to as witnesses.
“They were seen to be taking video footage and this could be crucial evidence. If you recognise yourself or someone you know in this footage, then please get in touch.”
Meanwhile, six England fans appeared in a French court just days later and were given sentences of between one and three months for their part in the fighting.
The NPCC warned any England supporters found to have been involved in the disorder could face football banning orders in the UK.
Assistant Chief Constable Mark Roberts, National Police Chiefs’ Council lead for football policing, said: “The violence in Marseilles was highly organised and those involved appeared determined to carry out sustained attacks at a level of aggression I have not encountered in the past 10 years.
“We are very aware that this involved a small minority of English supporters. Investigations will continue and these fans could be subject to a football banning order on their return to the UK.
“Our investigation team is on hand to assist the French police in any way that we can to ensure those involved are identified and prevented from engaging in further disorder.’