When Britain conquered Quebec at the end of the Seven Years War, Quebec began a transition between French law and English law. How did that transition occur?
British colonial rule after the end of the Seven Year's War ended in 1763 gave the Canadians, including those in Quebec, little choice. Since the British ruled, their laws became the law of the land. It really wasn't so much of a transition as it was an imposition, in that the British imposed it upon the Canadians.
In 1774, however, the British Parliament passed the Quebec Act in an attempt to ensure Canadian loyalty in the even that Britain went to war with the American colonies. This act restored French civil law, but retained English criminal law. In addition, the Catholic church was once again recognized and permitted to operate openly, and the French language was given official approval.
From 1840, Montreal politics were controlled primarily by English Protestants who tended to favor the British Laws. From 1873 to 1914 there was a transition of power that saw more French Canadians taking part in local government. After 1914, there was basically little or no English influence on politics.
Throughout all this time, even though the British ahd greater political influence, the legal structure remained basically the same. The civil law was based on the French Laws, while the criminal law was based on Enbglish Laws.