What would have happened if Napoleon had said “NO!” to the Louisiana Purchase?
This is, of course, a matter of speculation. There is no way to actually know for sure what would have happened. My own view is that the US would have gradually taken over the land west of the Mississippi because France was not in a position to do much with it.
Thomas Jefferson worried when Spain gave Louisiana to France because he thought France might use the land as a base for imperialism in the Americas. France did in fact want to do this. It wanted to use the land as a source of crops to feed its colonies in the Caribbean. However, by the time that 1803 rolled around, France had already failed in its attempt to take Haiti back from the rebellious slaves who had taken the country over. Without Haiti to feed, Louisiana was less important to Napoleon. Moreover, he was more interested in fighting in Europe and needed troops there, not in the New World.
This is why I think the US would eventually have taken over Louisiana. Napoleon would have been preoccupied with fighting in Europe. Eventually, he would be defeated and France would not be nearly as powerful as it had been. France would not have been able to prevent American settlers from moving into the Louisiana Territory. Eventually, that land would have become American because the US was the country that was in the best position to occupy and hold it. Therefore, I do not believe that it would have made much difference if Napoleon had refused to sell Louisiana to the US.