Germany will play England at Wembley on Sunday in the Euro 2022.
Popp put Germany ahead with a volley from Huth's cross from the right side of the penalty area for her fifth goal in five games.
Their lead only lasted four minutes before Kadidiatou Diani broke free and shot from outside the penalty area, with her effort hitting the post and bouncing in off the unfortunate goalkeeper.
The winner was decided when Popp headed in her sixth goal of the tournament after the Germany goalkeeper made three crucial saves.
The match at Wembley could set a new attendance record for a European Championship match, either male or female, and it will be held at a sold out stadium.
England, looking to win the tournament for the first time, thrashed Sweden, the highest ranked European side, by four goals.
There had been fears that the rail strike would affect the attendance at Stadium Keynes.
The match between two of the top five ranked teams in the world was played in front of the ninth highest crowd in the tournament's history.
The only notable effort in the opening 40 minutes was Popp's 25-yard free-kick, which was pushed wide by France goalkeeper Peyraud-Magnin.
That changed when Popp became the first player in the competition to score in five consecutive games, continuing his remarkable tournament after a serious knee injury.
The crowd had produced a Mexican Wave, which was seen as a sign that things could be better on the pitch, but that Popp volley sparked the game into life.
The first goal Germany have conceded in the tournament came four minutes later when Diani hit the back of the net after her shot struck the post.
France had three chances in a three-minute period in the second half to take the lead.
First off, Diani did a great job getting to the byeline, and she found a substitute who spun and shot, but it was parried.
The captain of France almost got her first goal of the tournament when she rose superbly at the back post and headed for goal, but her attempt was saved by the legs of the opposing goalkeeper.
For the first time in this tournament, Germany were looking vulnerable.
When they needed inspiration, it came from captain Popp as she headed a ball into the net as her side came back to take the lead.
France, who lost in the semi-finals of both the World Cup and London Olympics, tried to get an equalizing goal that would have taken it to extra time.
They couldn't equalize for a second time as Germany held on to win the game.
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