The Red Devils sacrificed a lot of their attacking play in order to keep their opponents at bay, with the likes of Kevin De Bruyne and Jeremy Doku doing plenty of work in their own half.
Didier Deschamps's side had control of possession for the majority of the contest but failed to find a game-changing moment early on, with lots of efforts from outside the box failing to work Koen Casteels.
With the Belgians tiring, Les Bleus managed to break the deadlock as the full-time whistle approached, with Randal Kolo Muani's effort deflecting in off former Tottenham Hotspur man Jan Vertonghen.
France are now just three victories away from continental glory in Germany, whereas Domenico Tedesco's men will exit the competition at the first hurdle of the knockout stages.
Vertonghen own goal breaks Belgian hearts
After putting in a sensational defensive shift throughout the 85 minutes leading up to the game's defining moment, Belgium will feel hard done by the nature of which they have been eliminated from the competition.
Moving in off the left flank, Theo Hernandez moved across a retreating Belgian backline before finding Jules Kounde on the right, with the Barcelona man and N'Golo Kante eventually working the ball into the feet of substitute Kolo Muani.
The 25-year-old did excellently to wriggle around in the box and find a yard of space for his shot, which deflected off Vertonghen's knee, dipping over the diving Casteels to ensure that Deschamps's blushes were spared.
France saved by Hernandez heroics
Keen to prevent France from having too much space on the attack, Tedesco set up his Belgium side with a midfield pivot of Amadou Onana and De Bruyne, a duo that rarely escaped into the opposition half at points.
That all changed when the Manchester City playmaker was moved into a more advanced role during the second period, with the five-time Premier League winner feeding a brilliant ball through to Yannick Carrasco.
The winger was bearing down on goal and looked set to slot the Red Devils into an unlikely lead on the counter, however left-back Hernandez recovered remarkable to execute a last-gasp block.
France shooting on sight
Having failed to score from open play during the opening three matches of this competition, Deschamps would have been reassured by the amount of chances his France XI created in Dusseldorf.
That being said, Adrien Rabiot, Kylian Mbappe and Aurelien Tchouameni were all guilty of firing efforts well over the bar, when a little more composure could have led to a more comfortable victory.
Les Bleus peppered the stands instead of Casteels's goal, registering 16 shots off target over the course of 90 minutes, managing just two on net.
Record-breaking evening for Vertonghen
What's next for France and Belgium?
Following a narrow success in Dusseldorf, France will fight for a spot in the semi-finals of Euro 2024 against either Portugal or Slovenia on Friday night.
As for Belgium, a round-of-16 exit means that Tedesco's major tournament debut has ended on a sour note, with the Red Devils back in action in September, when they will commence their UEFA Nations League campaign versus Israel.