The Louisiana Purchase
That land was claimed by France. Napoleon agreed to sell it to the US to get money he needed to fund his wars in Europe.
Before becoming part of the United States, the Louisiana Territory was claimed by France and Spain. Initially, France established control over the territory in the early 18th century, but it ceded the land to Spain in 1762. France regained ownership briefly in 1800 before selling it to the United States in the Louisiana Purchase of 1803.
We have no idea. The only US state that became a state in 1819 was Alabama. It wasn't "purchased", it was part of the Mississippi Territory, which had been claimed by the state of Georgia before being donated to the US government. The state most commonly associated with the word "Purchase" is Louisiana, but a) the Louisiana Purchase occurred in 1804, and b) the state of Louisiana was formed from part of the area involved in the Louisiana Purchase in 1812, both well before 1819, so it seems unlikely that's what you're referring to.
the french had claimed most of the us... the Louisiana purchase in mid 1800's gave 1/3 of the US back to the (primarily English) settlers
Illinois was acquired from Britain as part of the treaty ending the Revolutionary War which was before the Louisiana Purchase. The French had earlier ceded Illinois to the British with the treaty that ended the French and Indian War.
You have a misunderstanding here. Louisiana purchased nothing, the US purchased the territory that France identified as Louisiana which was much larger than the modern state of Louisiana. French Louisiana included all lands west of the Mississippi river except the southwest (claimed by Spain) and the Pacific northwest (claimed by England and Russia). However the precise boundaries of the Louisiana Purchase were (and still are) uncertain.
False
The Louisiana Purchase in 1803, in which the US bought land the French claimed in central North America.
it still had many people there
Louisiana.
The Louisiana purchase nearly tripled the size of the us