One way that this influenced the course of Canadian history was by making it less likely that the Canadian colonies would join in the American Revolution. The French-Canadians were very suspicious of the British colonists and did not have any desire to become part of a United States that would be overwhelmingly English. (Also, the Americans were very suspicious of the Catholic French.)
Today, this affects Canada mainly through the constant calls for independence for Quebec and for equality for Francophones. This (one can argue) weakens Canadian solidarity and helps give more power to the provinces.
Canada and the lower 13 colonies became a source of competition and an eventual battleground between the French and British empires. Since they both had settled the land, they both had their eye on exploiting its resources. This would lead to countless skirmishes, the French and Indian War, and it would lead to the French recognizing the United States in the Treaty of Alliance.
Today, Quebec, the maritime provinces, Saskatchewan, Alberta and British Columbia are all distinctly different cultures and economies. These divisions started with British and French colonization and are still visible today.