France want Rugby World Cup referee Jaco Peyper to be investigated after he was pictured mocking the red card he awarded Sebastien Vahaamahina for an elbow on Wales' Aaron Wainwright.
Peyper sent the Clermont lock off early in the second half of Sunday's quarter-final defeat by Wales.
But the South Africa official invited controversy after a picture emerged on social media showing him posing with Welsh fans and playfully landing an elbow on to the head of one.
French Rugby Federation vice president Dr Serge Simon said on Twitter: "This photo if it is true is shocking and explanations will be necessary."
A World Rugby spokesperson has responded: "World Rugby is aware of a picture on social media of referee Jaco Peyper with a group of Wales fans taken after last night's quarter-final between Wales and France in Oita. It would be inappropriate to comment further while we are establishing the facts."
Wales head coach Warren Gatland and his France counterpart Jacques Brunel endorsed the decision to issue the red card, and on Monday Gatland played down the fuss surrounding Peyper.
Asked about the picture, Gatland said: "Yes, I've seen that. I don't really know how to answer that question.
"He's had his 50th cap, he's posing with a few fans and he's making a bit of a joke about the incident in the game.
"How people interpret that is up to them. Obviously, the way things are and how PC everyone is, people like to make mountains out of molehills. That's how I view the situation at the moment."
World Rugby announced Vahaamahina will face a disciplinary hearing on Thursday following his dismissal.
He will appear before an independent judicial committee chaired by England's Mike Hamlin.