Natalie Achonwa of Guelph, Ont., added 14 points and eight rebounds for Canada, which is 1-2 in London with two pool games remaining against Brazil and Australia.
Emilie Goubis scored 16 points and Isabelle Yacoubou added eight of her 14 in the fourth quarter to help France advance to the quarter-finals.
France (3-0) was coming off a shocking overtime victory over Australia on Monday.
Yacoubou's consecutive lay-ins to start the final period gave the French a 46-40 advantage. Canada was able to cut it to 62-60 after Anchonwa's three-point play with 9.5 seconds left. Celine Dumerc sealed the win with two free throws less than a second later.
France made all 10 of its free throws in the final 1:27, including six by Dumerc.
Kim Smith of Mission, B.C., contributed eight points and played a game-high 29 minutes.
Canada plays Brazil on Friday and Australia on Sunday.
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