If the Louisiana Purchase had not taken place, the United States would not be one country from coast to coast. We would have a territory of France in the middle southern section of the United States. That territory would have a separate government, with its own laws, military, and law enforcement. A French territory would not be subject to the United States government at all. Trading between the French territory could only happen through treaties between the United States and France. To travel through the territory to go to a part of the United States on the other side, one would need a passport and a visa. Since the United States and the territory would share the same Gulf Coast, many issues could arise, for example, the issue of territory for fishing, the issue of border protection, and the issue shipping. Presumptively, the people in a French territory would speak French, thus requiring people along the border to learn French, too, or requiring the need of translators for many situations. There are, I am sure, other implications, but this should be enough to get you started.