The mercurial scrum-half limped off the pitch just before the half hour after his knee buckled under pressure from the Irish defence at the back of a ruck.
"I don't have good news. He's got a knee injury and he could not get back on to the field," Galthie said at half-time.
"We're suspecting something serious. He's suffering," he added in the post-match news conference.
Galthie said France had recommended that the two Irish defenders who made contact with Dupont -- Tadhg Beirne and Andrew Porter -- should appear before the disciplinary commission.
"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.
"I'm not going to pass judgement on the quality of the refereeing today," he added when asked about Australian official Angus Gardner's decisions.
Ireland interim coach Simon Easterby said that while he would probably have to look at the incident again, his coaching team felt Gardner had made the right decision in deeming no foul play.
"I think it's just a rugby incident where Tadhg cleans out someone in front of Antoine Dupont and he gets hit on the back of that," he said.
"This happens unfortunately. We definitely have moved away and players have a real awareness now of cleaning out on the lower limb of a player, which could create that type of injury that might have happened today, but that wasn't the case."
