Denver is a part of the Platte River basin that in turn feeds into the Mississippi River basin (other parts of Colorado are sources for many of the other major U.S. river basins). The Platte River basin is part of the Louisiana Territory as the French had claimed the entire Mississippi River basin as their own. The territory of Colorado that is west of the Continental Divide and much of Southern Colorado, in contrast, was not part of the Louisiana territory. Much of that territory was part of "Old Mexico".
Here is a nice map of that river basin via a Facebook post by John Orr whose blog is Coyote Gulch.