A brilliant first-half display and gutsy second-half showing amid a flood of cards handed Les Bleus only their second win over the Springboks in their last 11 Tests.
Captain Antoine Dupont was named man of the match in a pulsating encounter that contrasted the running invention of the French with South Africa's bludgeoning force.
And in the end, the only difference was a missed conversion by Springboks replacement fly-half Manie Libbok.
France, though, were almost undone by wayward kicking, especially from half-back Maxime Lucu.
The hosts' backs sparkled in the first half with the back three of wings Aaron Grandidier-Nkanang and Louis Bielle-Biarrey, and full-back Theo Attissogbe scoring a try each in a scintillating first half.
But South Africa's brute force and forward power kept them in touch, scoring two catch-and-drive tries.
Tries from hookers Jan-Hendrik Wessels and Malcolm Marx, and a close-range effort from replacement scrum-half Cobus Reinach, helped them storm back from a 21-7 half-time deficit, but it was not enough.