Name given to the area of French control in the New World?

From the first explorer, Jaques Cartier, to explore the St Lauwence in 1534 to the Defeat and secession of France after the 7 years war in 1763; (This war effectively ended militarily in North America in 1759 after the British victory at the Battle of the Fields of Abraham.) The land surrounding the St Laurence seaway and north and west of the 13 English colonies on the eastern seaboard was known by the French empire as New France, and colloquially it was known as as Quebec and Kanata.