France is out of the European Championship, and it was Kylian Mbappe that missed the penalty kick in the shootout.
Switzerland eliminated the World Cup champions 5-4 in the shootout after a 3-3 draw on Monday in the round of 16.
Switzerland goalkeeper Yann Sommer, who left the team during the group stage to be with his wife for the birth of their daughter, made the decisive safe on the 10th penalty after the previous nine had all been successful.
The Swiss will next play Spain in the quarterfinals in St. Petersburg on Friday.
It was the third game in the round of 16 to go to extra time but the first to be decided by penalties.
Switzerland substitute Mario Gavranović forced extra time with a 90th-minute equalizer.
Haris Seferovic put Switzerland in the lead with a header in the 15th minute as France struggled to work itself into the game. But that all changed early in the second half when the Swiss were awarded a penalty.
France goalkeeper Hugo Lloris, the team’s captain, made the save on Ricardo Rodríguez in the 55th minute and woke up the French. Karim Benzema scored once in the 57th, and again in the 59th to give France the lead.
Paul Pogba made it 3-1 in the 75th with a right-foot shot from 20 meters and it looked like the game was out of reach for the Swiss. But just as quickly as France had taken over the game, they let it go again.
Seferovic scored another header in the 81st minute and Gavranović made it 3-3 with only seconds remaining.