Although France had led most of the way, Canada got the gap back to just two in the final seconds before 'Les Bleus' experienced guard Celine Dumerc wrapped it up from the free-throw line.
France built an early advantage and were up 11-4 after Sandrine Gruda split a pair of free throws.
But by the start of the second quarter, Canada had come back to hold a brief lead and the teams remained close throughout the second and third quarters.
France started the fourth quarter with a two-point lead but quickly made it 50-43 on Isabelle Yacoubou's free throws before Canada came back again.
They had chances to tie down the stretch but, in a game where neither team hit a single three-pointer despite a combined 16 attempts, 11 by Canada, they could not make their shots.
With the gap at five going into the final minute, Canada began to foul. Dumerc and Emilie Gomis kept their cool at the free throw line for the French.
But Canada were given late hope when Natalie Achonwa got the rebound from a missed free throw and dropped it in to make it 62-60 with nine seconds left.
Canada got a quick foul, but Dumerc iced it from the line to secure the win.
Gomis led France with 16 points and Yacoubou added 14. Shona Thorburn had 17 for Canada with Achonwa adding 14.