The hosts won 1-0 thanks to Jean-Philippe Mateta's early header but the quarter-final was overshadowed by a brawl after the final whistle.
Enzo Millot was sent off in the aftermath for allegedly goading the Argentinian bench.
It came after Argentina's players sparked a race row following their Copa America triumph.
Chelsea midfielder Enzo Fernandez filmed several of them singing a disgusting song which alluded to some France stars' African heritage.
Tensions between the countries have been high ever since and the French squad were filmed gesturing towards the Argentinian support after reaching the Olympic semi-final.
Fans took to social media to share their thoughts on the French celebrations.
One wrote as cited by Sports Central: "ABSOLUTE CINEMA."
Another commented: "This is how we respond to racism! Long live France."
A third posted: "And it is well deserved. And without disgusting songs."
Following their win, French coaching staff and players spilled onto the pitch in celebration at making an Olympic semi-final on home soil.
While Argentina coaches and substitutes were also seen running onto the playing surface.
There was clear pushing and shoving as a group of Argentine players confronted France star Millot.
As things escalated, other players got involved in a bid to try and calm things down.
According to reports, France midfielder Millot had celebrated his nation's victory over-zealously towards Argentine players - sparking an angry reaction.
And after the match, French manager Thierry Henry revealed Millot had been shown a red card and fumed at his player's behaviour.
Arsenal legend Henry said: "I apologise for the final disturbance. It's not what I wanted and I couldn't control it. "Enzo Millot received a red card after the match. That's not helpful. "I don't like this kind of thing. I'm not happy about it."
After a row erupted last month over Fernandez's video, Chelsea teammate Wesley Fofana, who is French and the son of an Ivorian father, took to social media to slam the clip as "racism".
He wrote: "Football in 2024: uninhibited racism".
Fernandez has since issued an apology online to those who saw the video, as well as a private apology to his Chelsea teammates.
And Fofana revealed that he and Fernandez have made up, explaining that the South American is "not racist".
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