What role did napoleon play in helping unites states grow larger?

Answer 1

The rising French empire had been crippled from its recent French Revolution. France badly needed money.

Meanwhile, their old friends in America were dreaming of something called "manifest destiny." Essentially this meant western expansion.

And so Jefferson and Napoleon found it would be in both their nations best interest to trade off France's territory in the United States (with so much turmoil to deal with in Europe, the land had become useless to France).

In France this sell-off is called the "Vente de la Louisiane." For Americans, this pivotal is called the "Louisiana Purchase."