Le Court, who became the first African rider to win a stage in the Tour on Wednesday, caught up to the chasing group on the final descent into Chambery to finish sixth and retain the yellow jersey.
“I wasn’t feeling so good since the start of the stage, the last few days I’ve been going through some stuff,” said the 29-year-old from Mauritius.
“On the last climb it was difficult, my body just shut off. Then I had to do the best downhill of my life.”
France’s Pauline Ferrand-Prevot remains second in the general classification, with defending champion Katarzyna Niewiadoma-Phinney third and 2023 winner Demi Vollering just behind.
The top five in the general classification are separated by 35 seconds with two stages remaining.
On Saturday the riders will tackle a 111.9km mountainous stage between Chambery and Saint Francois Longchamp-Col de la Madeleine.