Everton on Friday banned a fan who appeared to try and strike a Lyon player while holding a child during their Europa League match as police probed crowd trouble at Goodison Park.
Thursday's ugly scenes erupted after Ashley Williams barged into Lyon goalkeeper Anthony Lopes midway through the second half of the 2-1 victory for the away side, sparking a melee.
Fan pushes, hits Lyon goalkeeper Lopes
That skirmish moved to pitch-side advertising hoardings, at which point a man carrying a child pushed Lopes in the head before hitting out at him again.
"Club officials have reviewed the footage of an incident that occurred in the 64th minute of the game against Olympique Lyonnais where supporters towards the front of the lower Gwladys Street End became involved in a confrontation between players," Everton said in a statement.
"We have identified one individual whom action will now be taken against. This will include a ban from attending future Everton fixtures and the club registering a formal complaint with Merseyside Police."
The police issued their own statement, which confirmed they were also looking into the matter.
"Merseyside Police can confirm officers are investigating following a disturbance on the pitch during a football match between Everton and Lyon at Goodison Park last night, Thursday 19th October," they said in a statement.
"Detectives will be reviewing footage and speaking to witnesses to establish what, if any, offences have been committed."
European governing body UEFA is likely to take action after the skirmish and both Everton and their defender Williams, who was captain for the match, could face sanctions.
Williams shove on Lopes sparks fracas
Williams instigated the ugly scenes when he shoved Lopes off the pitch as the goalkeeper went up to make a catch on the byline.
Numerous Lyon players reacted angrily and a fracas broke out involving players from both sides, with the trouble even spilling into the crowd as the huddle reached the advertising hoardings.
Williams was booked for his role and appeared fortunate to escape with just a caution as replays showed he raised his hands to Lucas Tousart's face.
"It's what happens, it's football. It is what it is," said Williams after the game. "It's high emotions. We want to win the game, they want to win the game and stuff happens. That was just one of those times."
Toffees manager Ronald Koeman blamed referee Bas Nijhuis for his players losing their cool during a defeat that leaves Everton facing Europa League elimination after just one point from three games.
"I think the irritation grows in the game for our players and in my opinion that was the problem by the referee," Koeman said.
"The referee was Dutch but he didn't do anything against the theatre of some of the Lyon players. [Nabil] Fekir in the first half dived 10 times. I understand with my players, that comes out of frustration."
It compounded another miserable night for Everton and Koeman, who is under mounting pressure with his team having won just two of their previous 12 fixtures.