Kick-off was delayed by more than 30 minutes as a number of ticketless fans forced their way into the stadium while many more with genuine tickets were prevented from entering.
Police resorted to the use of tear gas and pepper spray to disperse frustrated crowds at the gates.
Real Madrid, who won 1-0 on the night, have said that their own fans were caught up in the disturbances and want explanations to what occured.
An official statement from the club read: "In light of the unfortunate events which took place on the 28th of May in the surroundings of and at access points to the Stade de France, and even inside the stadium itself, Real Madrid C. F. wishes to express the following in defence of our fans, who were victim to said events.
"We would like to know the reasons which led to this venue being chosen to host the final and the criteria used, taking into account the experiences of the day.
"Furthermore, we call for answers and explanations in order to determine those responsible for leaving the fans abandoned and defenceless. Fans who in general terms showed exemplary conduct at all times.
"We believe something which should have been a wonderful festival of football for all fans who attended the game, quickly turned into a series of unfortunate events which have caused a sense of outrage around the world.
"As was evident in the revealing images published by the media, several fans were attacked, harassed, assaulted and robbed in violent fashion. These occurrences continued as they moved in their cars or busses, causing concern for their physical wellbeing. Certain fans even had to spend the night in hospital as a result of injuries.
"Football has transmitted an image to the world which is far away from the values and goals which it should pursue.
"Our fans and supporters deserve a response and those responsible to be held accountable in order for events like these to be eradicated from football and sport in general."
