The Netherlands received a dream message ahead of the match as star Vivianne Miedema was back after missing two matches due to covid-19.
However, it was France that took hold of the match, and offered a cavalcade of chances in the first half.
Double saves on the goal line
The closest they came in minute 36 when centre-back Stefanie van Der Gragt acted as goalkeeper and saved Meline Malard's shot on the goal line.
Five minutes later she repeated the feat, this time after a finish by Grace Geyoro.
- France excels.
They are worth a goal, said SVT's expert Daniel Nannskog during the break.
Extension required
France continued to lay on and just before full-time Geyoro burned another great chance when she headed wide from close range.
It took extra time, and a penalty, to salvage the win.
Dominique Janssen brought down a free Kadidatou Diani and the referee pointed to the penalty spot after VAR review.
Ève Périsset slotted the penalty safely into the goal post, and the win was a fact.
Germany awaits France in the semi-finals.