The 25-year-old Thiney headed in from close range after 24 minutes and added another with a thundering 20-metre strike before goals from Camille Abily and Elodie Tomis condemned Canada to a second successive defeat in the tournament.
"That was a fantastic performance," France coach Bruno Bini told reporters. "It was difficult at the start but we recovered well."
"The whole team played brilliantly. We raised the level when we needed to and were were very strong technically."
Canada began brightly and created an opening on 13 minutes when Sophie Schmidt slipped a pass into the run of Diana Matheson but her poor first touch allowed keeper Berangere Sapowicz to smother.
France, 1-0 winners over Nigeria in their opening game, gradually took control and with the Canadian defence looking out of sorts, struck after 24 minutes with Thiney heading in from 10 metres after Elise Bussaglia's cross was deflected and Canada twice failed to clear.
With Canada's defence in tatters, France were unlucky not to add another in the first half as forward Marie-Laure Delie dominated in the box, going close on three occasions.
"We made too many individual mistakes," said Canada's Matheson. "If you don't score then you can't win."
"Unfortunately we did not win the battles that it took today."
Delie should again have scored early in the second half when she broke free only to see her shot smothered by keeper Erin McLeod.
Thiney, courtesy of yet another defensive error, quickly made amends with a powerful drive that flew in off the post.
Canada captain Christine Sinclair, wearing a head mask after breaking her nose and playing on against Germany, did her best to lift her side but Avily made it 3-0 when she drilled in a Sandrine Soubeyrand corner in the 67th minute.
Tomis then showed off her pace, beating two defenders and rounding McLeod for France's fourth goal.
"We were outstanding. It is all about the team and everything went right for us," Thiney said.
