The Seven Years War, in which England and Prussia triumphed over France, Austria, and Russia, concluded in 1763. That year, the Treaty of Paris gave England control of French Canada as well as Florida.
In the same treaty, France gave Spain all of LaSalle's claim of 1682, which created a Spanish empire in the Western Hemisphere that extended all the way from the 50th parallel in North America to Cape Horn at the southern tip of South America.
Twenty years later, in 1783, Great Britain gave back to Spain all the territory east of the Mississippi and south of the 31st parallel. Then, in 1800, by the "secret" Treaty of San Ildelfonso, Spain gave all of LaSalle's Louisiana back to France, including "the Floridas," which Spain had claimed since 1492.