Thiney scored in the 24th and 59th minutes, and Camille Abily's header from a corner kick put the outcome beyond doubt in the 66th before 16,591 fans. Substitute Elodie Thomis added the fourth goal in the 83rd, rounding the goalkeeper after being set up by playmaker Louisa Necib.
Canada captain Christine Sinclair was unable to exert her usual influence. She wore a mask after breaking her nose in the previous game, a loss to Germany.
''Maybe if Christine was at 100 percent, we would have been able to maintain more pressure up front,'' said Canada coach Carolina Morace.
Germany was to play Nigeria in Group A's late game, where a win for the host would leave it level on points with France, with Canada out.
''Skills made the difference,'' France coach Bruno Bini said. ''The goal is to have the whole team play well.''
Canada's defense was at fault for the first goal, when Elise Bussaglia's shot deflected to the unmarked Thiney, and the winger's cushioned header gave Erin McLeod no chance.
Another mistake allowed her second when Marie-Laure Delie caught Emily Zurrer in possession and fed the ball back for Thiney to shoot in off the right post.
''Everything worked right for us today,'' Thiney said. ''My goals were fantastic.''
When Jonelle Filigno tripped over the ball in front of goal in the 65th, it seemed certain not to be Canada's day, with Abily scoring a minute later.
Canada managed only two shots on goal in the first half, compared to 11 for France.
Morace's side was restricted to chances from free kicks after a scrappy start to the game - Rhian Wilkinson's cross was gathered comfortably by Berangere Sapowicz - before Diana Matheson hesitated and lost the chance after she was played through by Sophie Schmidt in the 15th.
France's tactic was to play the ball forward as quickly as possible to the pacy Delie, and McLeod had to be alert to gather from the onrushing 23-year-old more than once.
Only McLeod's acrobatic save prevented Necib's 20-yard lob from creeping into the top corner in the 31st, before Delie headed over under pressure from the Canada keeper.
Canada's troubles were evident in the 57th when Sinclair played a good ball for Kaylyn Kyle in space, only for the midfielder to rush her shot after failing to control the ball.