After the game finished 0-0 following extra time, Joao Felix hit a post with a penalty in the shootout and Theo Hernández converted the clinching kick.
Portugal head coach Roberto Martinez consoles Cristiano Ronaldo after the quarterfinal loss. (EPA PHOTO)
Portugal had the best chances to take the win during regular time, forcing goalkeeper Mike Maignan into two big saves to deny Bruno Fernandes in the 61st minute and then Vitinha in the 63rd.
But the 0-0 stalemate persisted after extra time and the Portuguese side were faced with a second consecutive shootout, following a 3-0 win on penalties against Slovenia in the last 16.
It was a record sixth European Championship for the 39-year-old Ronaldo, who scored Portugal's first penalty in the shootout and ended up consoling fellow veteran Pepe afterwards as the 41-year-old defender cried on his captain's shoulder.
"We need to go through this moment of our loss, which is very painful," Pepe said.
Ronaldo's 20-year career in the Euros included the title in 2016 - Portugal beat France in the final - and it remains to be seen if the five-time world player of the year will continue playing for his country through to the 2026 World Cup, when he will be 41.
"Everything is too raw," said Portugal coach Roberto Martinez, when asked if that was Ronaldo's last game for his country. "We are suffering a defeat as a team - there are no individual decisions at this point."
The victory ended Kylian Mbappé's and France's recent heartbreak in shootouts, having lost in them at their last two major tournaments - in the last 16 at the Euros in 2021 and in the 2022 World Cup final.
Mbappé didn't even take a penalty in the shootout, having been substituted after the first half of extra time following a couple of knocks to his broken nose that was covered by a protective mask.
Les Bleus didn't need their star player, as Ousmane Dembele, Youssouf Fofana, Jules Kounde and Bradley Barcola all found the net in the shootout - held in front of Portugal's fans - before Hernández's coup de grâce set off jubilant scenes for the French inside the stadium in Hamburg.
"It wasn't easy," France goalkeeper Mike Maignan said. "We didn't always play that great, it was a complicated game. We played well defensively."
"We got to the penalty shootout and didn't waver. We can be proud of ourselves."
Didier Deschamps' team has reached the semifinals despite no France player having scored from open play so far in the tournament.
Portugal exited having failed to score in either of their knockout games - the team beat Slovenia on penalties in the last 16 - and in their final group match, leaving Martinez plenty of questions to answer.
"From our side, we deserved to win," Martinez said. "But we are talking about the best players in Europe. It's a sad night."
France will play Spain in the semifinals after their extra-time win over Germany in Stuttgart earlier.
