The South Africans fought their way back from a 24-18 half-time deficit to finish the match with a total of five tries to four by France, which earned them a bonus-point win and the last semifinal place up for grabs.
The team entered the match needing a victory with 14 points to secure a semifinal place, while they had to ensure that Australia did not register a big victory against England, as their match played out at the same time.
Theron says: “I am proud of the fighting spirit the players showed.
“There were times when we allowed France to apply immense pressure on us, but the team showed fantastic character to bounce back after half time and to earn the bonus point.
“That said, we have a lot of work to do before we meet England.
SA will face England in the semi-finals next Monday (8.45pm), while Ireland and Argentina will square off in the other playoff on the same day (6.30pm)