Geographical connection is important, especially in that era. It made annexing and incorporating the land into the nation realistically impossible for France. France sold the land, that shows you how important it was to the Nation of France, and it also brings up an important difference in the governments of France and the United States.

When the Louisiana purchase occurred the United States was a Federation, each state were their own distinct autonomous nations in many respects (now less so as the Federal government has claimed and asserted more and more authority, but we are discussing the early 19th century here). There were roughly two dozen Senators selected from the states and each one of these men held a great deal of power, not to mention the fact the Executive branch changed it's head (the president) and cabinet every 4 to 8 years: The United States simply could not develop a coherent imperial policy to form overseas holdings and extract resources from to the developed "motherland" because of the nature of it's government. Many of the Congressional representatives came from slave holding rural states that would have been wholeheartedly against the competition colonies represented. Because of this the United States took a direct conquest approach, it used overwhelming technological force and manpower and underhanded diplomacy (it constantly broke treaties with tribes in it's path of expansion) to simply take the land. Once the land was controlled by the United States congress was never unified enough to produce a policy to really form mercantile colonies (and the executive at this time was a neutered version of what the Presidency is now). The path of least resistance was simply what happened; the land was settled, developed by private interests (for the most part, congress did occasionally pass acts to support infrastructure and development of the western territories, but by and large these acts were based on private interests taking advantage of things like homesteading). Later, when these territories were fully developed they were incorporated into the Federation. This is absolutely nothing like what was going on in France politically or economically in terms of it's colonies, for starters France was an autocracy during this entire period, but also it's holdings were overseas and it had no way to simply encourage private interests to settle the land, nor was there any clear path to incorporating Lousiana into the Nation of France.

The geographical facts are important aspects of why colonial expansion isn't applicable to the United States in terms of western expansion. It's part of the reason why it is different, and not a reason for it being similar.