France are yet to score from open play in four matches at the tournament – captain Kylian Mbappé netted once from a penalty against Poland, while their other two goals came from opposition defenders.
Crucially, however, they are rock solid in defence, having conceded only one goal, from a penalty, so far.
Their back line was outstanding against Romelu Lukaku and his fellow attackers, and Belgium bow out after what will go down as a disappointing tournament for them.
Both of these sides were looking for revenge, in Belgium’s case for their 1-0 defeat against France in the semi-finals of the 2018 World Cup, a result that still hurts six years on.
France, meanwhile, had a point to prove at the Euros after going out in the last 16 three years ago on penalties to Switzerland, a deeply disappointing result in between runs to consecutive World Cup finals.
The French were widely seen as the favourites to win this tournament before arriving in Germany, but they were below par during the group phase.
The broken nose suffered by Mbappe in their opening game against Austria did not help, and the uncertain form of Antoine Griezmann has been a problem too.
Griezmann was dropped for the last group match against Poland but returned here in one of two changes, with Marcus Thuram also coming in as wingers Ousmane Dembele and Bradley Barcola made way.
Meanwhile Belgium coach Domenico Tedesco’s reaction to his own side’s unconvincing displays in the group stage was striking.
Yannick Carrasco and Lois Openda were given starts to provide as much attacking threat as possible in support of Lukaku, while skipper Kevin De Bruyne played a more withdrawn role.
The hope, for the neutrals at least, was that so much attacking talent would lead to an open game full of goals, but the reality was rather different.
Belgium were happy to sit back and thwart France, and did not test opposition goalkeeper Mike Maignan at all in the first half.
France had lots of the ball, yet often looked untidy, imprecise and rather flat, with Griezmann appearing lost on the right wing.
But they had chances in the first half, with Thuram heading just wide from Jules Kounde’s inviting cross just after the half-hour mark and Aurelien Tchouameni twice firing off-target.
Real Madrid midfielder Tchouameni then tested Casteels with a deflected long-range strike as France upped their game at the beginning of the second half.
Mbappe accelerated inside and smashed a shot just over, and there was a sense a goal might be coming.
The breakthrough almost came for Belgium an hour in as William Saliba lost possession on halfway and De Bruyne released Carrasco, who was about to pull the trigger when Theo Hernandez arrived to make a brilliant saving block.
Maignan finally had to make a save 20 minutes from the end of normal time, to keep out a drive from Lukaku, and was called into action again to deny De Bruyne.
It was becoming clear that one goal would decide the contest, and France got it in the 85th minute as N’Golo Kante fed Kolo Muani, and his shot went in off Vertonghen to take Les Bleus through.
