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.
The Swiss will next play Spain in the quarterfinals in St. Petersburg on Saturday.
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.
It was the third game in the round of 16 game to go to extra time but the first to be decided by penalties.