Crystal Palace's Jean-Phillipe Mateta headed in from a cross from his former club-mate Michael Olise five minutes in, and that ultimately proved enough for Thierry Henry's men to progress.
VAR disallowed France a second late on, but Argentina could not make their fortune count before tempers boiled over between the players at the final whistle.
Argentina came out on top in the 2022 World Cup final between these great footballing nations, and there were an equal amount of thrills and spills this time around.
Mateta's early goal set the tone for a dominant display from Les Bleus in the first half, with Enzo Millot going close before Geronimo Rulli denied France's goalscorer a second.
While Giuliano Simeone should have done better before the break, it was a similar story in the second half as Mateta again met an Olise corner, but this time his header went just over.
Olise seemed to have capped off a virtuous display with a goal of his own 10 minutes from time, but VAR disallowed the goal for a foul in the build-up.
Loic Bade struck the woodwork just after, and Claudio Echeverri - just on as a substitute - may have made France pay had he kept his composure with the goal gaping, only to slice over as Les Bleus held on to set up a semi-final against Egypt, who beat Paraguay 5-4 on penalties.
Data Debrief: France's Palace connection
Two players who starred at Selhurst Park last season were the main men in Bordeaux on Friday.
He was a constant threat, taking the most shots for France (three) and contributing 0.35 of their 0.97 expected goals (xG), while also having the joint-most touches inside the box (four, level with Olise).
Olise shone in a central role behind his former team-mate, creating three chances, the joint-most of any player in the match.
There has been plenty of excitement around the home nation heading into the men's Olympic tournament, with coach Thierry Henry selecting a strong squad even with superstars like Kylian Mbappe absent.
Yet it took more than an hour for the match in Marseille to spark into life, and even then France were reliant on a moment of magic from captain Alexandre Lacazette.
The United States were the better side up until Lacazette's breakthrough goal, with Djordje Mihailovic thundering against the crossbar shortly before the veteran striker went up the other end and picked out the bottom-left corner.
A frantic spell followed in which France twice could have been pegged back, grateful first to Guillaume Restes for a superb save from Paxten Aaronson and then to the goal frame as John Tolkin headed against the post.
Instead, a second goal against the run of play settled the nerves in the stands as Bayern Munich new boy Michael Olise curled a fine finish around Patrick Schulte from outside the box.
And Loic Bade added further gloss with a header from a Joris Chotard corner five minutes from time, while Griffin Yow saw a late consolation goal struck off for offside.
Data Debrief: Belated home comfort for Les Bleus
On paper, the gulf between the two teams was evident in the scoreline, but for those home fans in Marseille who grew audibly agitated early in the second half, this was far from easy viewing.
Although France finished with three goals, they only created chances worth 0.43 expected goals (xG). The strikes by Lacazette and Olise were inspired individual efforts rather than the result of fine team play.
Winning gold as the hosts is not easy in this event – only four nations (Great Britain in 1908, Belgium in 1920, Spain in 1992 and Brazil in 2016) have done so previously in 27 attempts – but more will be expected of Henry's outfit going forward.
Les Bleus were minutes away from a semi-final exit against the Pharaohs until Jean-Philippe Mateta's 83rd minute equaliser.
Mateta would grab his fourth of the tournament in the ninth minute of extra-time, with former Crystal Palace teammate Michael Olise confirming the 3-1 win soon after.
Henry had been preparing for this event since taking over in August 2023 and felt the weight of responsibility, having seen his nation perform brilliantly in other events as the hosts.
“I’m living a dream. I don’t want to wake up," Henry said.
"I’ll be honest with you, what’s nice is for Team France because when you see everyone winning medals here and there, you think it’s up to us not to let the guys down.”
Henry endured a torrid time in charge of Monaco over five years ago, winning five of his 20 games in charge (D4, L11), but has since rebuilt his career.
Firstly, in the MLS with Montreal Impact, leading Montreal to their first playoff berth in four seasons, before returning for a second stint with the Belgium national side as an assistant manager.
This tournament has seen Henry possibly stake a claim for the France job further down the line, with Didier Deschamps’ contract expiring after the 2026 World Cup.
However, Philippe Diallo, president of the French Football Federation, did not want to entertain the idea just yet.
Diallo told RMC: “Let’s not rush things. Thierry Henry, when I appointed him to the position, there were some who had doubts given what he had done previously. I had confidence in him and he is proving it.”
France will play Spain at the Parc des Princes on Friday in the showpiece final.
France last triumphed in the competition at the 1984 games in Los Angeles, failing to reach the knockout stages at the Tokyo Olympics back in 2020.
But under the guidance of Thierry Henry, who scored 51 goals for Les Bleus during his international career, the French are among the favourites to scoop the top honour.
Henry's side have won two of their three pre-tournament friendlies this month, the latest result ending in a 1-1 draw with Japan, who won bronze in the 1968 games.
Lacazette was named by Henry as the nation's captain ahead of the competition, and will lead Les Bleus' star-studded line-up out against the United States in Marseille on Wednesday.
Jean-Philippe Mateta, Michael Olise, Rayan Cherki and Manu Kone are just some of the names at Henry's disposal.
Having not featured for Didier Deschamps' side since 2017, Lacazette explained that the squad are in unison of achieving gold at their home games.
"We all have the same ambition, to go all the way and win a medal," the 33-year-old said. "The fact that it’s a home games is really going to motivate us."
Henry has lost just two of his 11 games in charge of France's U21 and U23 sides (W7, D2) since being appointed back in August 2023.
Former Arsenal forward Lacazette said Henry wanted the team to play an attacking, possession-based style of football heading into the tournament.
"Tactically, he is decidedly forward-thinking... he especially wants us to enjoy ourselves and put on a show for the spectators,” Lacazette said.
Following their Group A opener against the United States, France will play Guinea and New Zealand.
