The Canadians, along with Slovenia, had accused the French team of changing the shape of the athletes' ski pants for better aerodynamics. Rules prohibit uniform alterations for such purposes.
Calgary's Brady Leman finished fourth in the final to Jean-Frederic Chapuis, Arnaud Bovolenta and Jonathan Midol of France in Thursday's competition. If Canada had won the appeal, Leman would have become the gold medallist.
Slovenia's Filip Flisar placed second in the small final and would have been bumped to bronze while Russia would have taken the silver.
The sweep by Chapuis, Bovolenta and Midol was France's first gold, silver and bronze in the same event at any Winter Olympics.
The top sports court's decision came on Sunday, the final day of the Sochi Olympics.