So far French authorities have largely blamed Liverpool fans for some of the problems, saying fake tickets were in circulation.
European football governing body UEFA said at the time that the game won 1-0 by Real Madrid had been delayed by over 30 minutes due to fans arriving late.
But on Wednesday after a cabinet meeting, French government spokeswoman Olivia Grégoire said: “I apologise. Can we do things better? Yes.”
She said President Emmanuel Macron wanted transparency around the chaos.
Two forms of investigation are underway with a view to not having a repeat at the 2024 Olympics, Grégoire said.
UEFA has also commissioned a report.
It has been reported that Macron is angry with Interior Minister Gérald Darmanin for initially blaming Liverpool supporters.
Police in Paris, who registered more than 100 arrests and 230 injuries around the final match, have been criticised by Liverpool fans for alleged heavy-handed tactics.