It was France who made the better of the early running, and Louisa Necib fired an effort wide with eight minutes on the clock.
The chances continued to fall for France early on, with Gaetane Thiney missing the target from inside the penalty area moments later.
Sinclair again came close 10 minutes later when she evaded the French defence, but she was just crowded out in the box at the vital moment.
Chances remained few and far between in the latter stages of the half, with both sides struggling to find their final ball.
France had a glorious chance to take the lead moments into the second period when Necib struck an effort from close range, but Erin McLeod made the save to her left.
France continued to control the second half, and Thiney thumped an effort against the post on the hour mark, before Elodie Thomis struck the crossbar moments later.
Canada just could not get into the match as the match developed, and Thiney had a goal-bound effort cleared off the line by Desiree Scott.
Corine Franco was next to come close after 78 minutes, but her strike was blocked by a combination of Canadian defenders in the area.
The chances continued to fall for France, but Eugenie le Sommer headed just wide in the final moments of normal time.