Dupont was attempting to steal the ball in the 28th minute and was challenged by Beirne, who then fell on to the scrum-half’s right leg as Irish prop Andrew Porter joined the ruck.
“We named the players [who made contact with Dupont], Tadhg Beirne and Andrew Porter, who should appear before the disciplinary commission,” Galthie added.
“We want explanations, so we’ve named two players. We have to protect our players. There are means, there are rules. There is some kind of anger.”
Ireland interim head coach Simon Easterby said the injury to Dupont, who was replaced by Maxime Lucu, came after a “rugby incident”.
“Tadhg [Beirne] cleans out someone in front of Antoine Dupont and he gets hit on the back of it. It happens, unfortunately,” said Easterby.
“We have moved away and players have a real awareness now of clearing out on the lower limb of the player, which can create that type of injury that might have happened today, but that wasn’t the case.
“He was securing his own ball and not making contact on Dupont. Unfortunately that happens. The guy that Tadhg hit was hit on to Dupont. It’s just one of those things unfortunately. It happens in the game.”
France play Scotland in Paris next weekend in what is the concluding game of the Six Nations championship, while Ireland will look to bounce back against Italy in Rome.
