Siya Kolisi and his team won 29-28 at the Stade de France, here are key quotes from those involved in the epic match.
Springbok captain Siya Kolisi on the win
"It was a hard game. We knew how tough it was going to be with the French team at home and honestly I just want to say well done to them for what they have achieved and how hard they worked."
"I just thought we really wanted it. I must give credit to the guys who came off the bench. They came and made a good defence."
Kolisi says support from back home has been the Boks' motivation
"Most importantly (we play for) the people back at home, honestly the support that we've received! You know they can't afford to be here but the videos of the schools singing for us, that's what we play for. We play for a nation, it's not about us... and that's what's driving us."
"There is a feeling of a lot of disappointment and frustration. It is sad and very disappointing for us. Yes of course we have a decent group of talented youngsters but we can assess the future later. For now it is hard to accept going out."
Flanker Francois Cros on France letting slip their chance on home soil
"We didn't give up anything in the match, we had all the ingredients but it's true that we conceded points too easily.
"But we can find whatever explanations we want, it's over for us and the adventure stops here. It's a pity because we deserved to go further. It's the competition of our lives, we won't play another World Cup in France and so it's a pity to end like this."
Bok lock Eben Etzebeth, who scored a second-half try
"That's right up there in my career, that was a brutal Test match. In the first couple of minutes they scored, then we scored and it went on like that - a one-point game!
"Obviously it is a relief inside me, the French must be heartbroken so thoughts to them. We will celebrate tonight and then prepare for the semi-final with England, it will be a massive game."
France team manager Raphael Ibanez on captain Antoine Dupont, who returned from a broken cheekbone to lead his team
"I think he is an amazing player. I think he has shown some courage over the last few weeks. We knew he could play at that level and he is a true leader so it's promising. Tonight is so hard for French fans and the team but we will be back."