Was The Louisiana Purchase about the state of Louisiana?

Not entirely. The Louisiana Purchase included a huge swath of land west of the Mississippi River -- the Louisiana Territory (French Le Louisiane) was nearly as large as the existing United States, including all or part of 13 current US states.

The intent of the Purchase was to acquire the port of New Orleans. Napoleon, unable or unwilling to maintain control of New France, offered to sell the entirety of the remaining French claims in North America.