It was almost solely due to their victory in the Seven Years War (or French and Indian War, for Americans), which saw them defeat the French in several different colonial theatres around the world, e.g. Canada, the Caribbean, West Africa, and India, and seize most of their colonies, most notably Canada and the Louisiana Territory (i.e. a vast swathe of land from Louisiana up to the Great Lakes and the border of Canada), which was fully conquered in the early-to-mid 1760s. Before this, British and French influence and power in North America was roughly equal, or at least no one country had a decisive superiority. The Spanish Empire had already conquered/claimed (but not heavily settled) all of the west and much of the mid-west, but they didn't expand any further east because of the French claims over Louisiana and along the Ohio River. Anyway, they already had more than enough territory in the rest of the Americas to be content with (much of which was also far more economically valuable). In the 18th century Spain was on relatively good terms with France, as they were both ruled by the same dynasty and were eager to remain friendly and occasionally allies to counteract British and Austrian schemes in Europe and abroad.

It's also worth noting the disparity in populations between the British and the French colonies in North America - the British Thirteen Colonies had roughly 950,000 settlers, while French Canada had no more than 60,000. That said, in the early stages of the Seven Years War the French achieved more military success because though they had a vastly smaller colonial population, they had more Native American allies, and almost every male adult in Canada was part of a local militia and thus already had some rudimentary military training and firearms experience. The British were only able to turn the tide of the conflict when many of France's Native American allies abandoned them, and when the British Royal Navy was able to achieve mastery over the seas and block food supplies and troop reinforcements from France (Canada was notoriously prone to famines in this era, and relied heavily on supplies from the mother country).

France very briefly recovered much of the Louisiana Territory in 1802 when it was ceded to them by Spain (a reluctant/forced ally of Napoleon's new regime), but French settlement of the region was extremely minimal, even compared to Canada, and the following year Napoleon famously sold the entire territory to the United States at an absurdly low price (he feared that the British would seize it if he didn't do this). Napoleon did briefly have ambitions of reasserting French influence in North America, but the outbreak of war with the United Kingdom in 1803-4 brought an end to this rather quickly - the British navy was simply too large and powerful to attempt anything that would require crossing their domain (i.e. the Atlantic).

Source: The Global Seven Years War by Daniel Baugh