Final answer:
The importance of La Salle's claim of the Mississippi Valley lay in establishing French control over the territory, which later factored into the United States' strategic acquisition of the land through the Louisiana Purchase in 1803.
Step-by-step explanation:
The importance of La Salle taking possession of the Mississippi Valley was significant in that it paved the way for French claims to the territory. La Salle's exploration and French claims did facilitate France's control over key strategic waterways in North America, which later on played into the negotiations of the Louisiana Purchase. However, the question seems to intertwine La Salle's exploration and France's eventual control over the Mississippi Valley with the Louisiana Purchase made by the United States.
René-Robert Cavelier, Sieur de La Salle, was an explorer for France in the 17th century who claimed the Mississippi River basin for France, naming it Louisiana after King Louis XIV. This was decades before the Louisiana Purchase. The actual Louisiana Purchase occurred in 1803, when the United States acquired the territory from France. This Purchase was significant because it doubled the size of the United States, gave control of the port of New Orleans, and ensured access to the Mississippi River, which was vital for the trade and westward expansion of the United States.
The exploration by La Salle did not give France land over Spain or England immediately but it did assert French claims in the region which held until the region was sold to the United States in the Louisiana Purchase. As for Spain, it never controlled all the rivers and lakes in North America; Spain had much influence in the region but the assertion that it had control over all waterways is incorrect.