In the late 1600s and early 1700s, the British were developing their trading companies in the Hudson Bay area and the Spanish were active in the southwest. The Upper Missouri Valley was part of the French colonial empire until 1763. Very little attention was paid to the region, however, as the French concentrated their efforts in the Mississippi River Valley.
While the Europeans were developing their holdings elsewhere, their trade goods were making an appearance on the plains near the Black Hills [1], as intertribal trading brought horses north to the hills and plains and brought other goods west from Minnesota. Beads, knives, and other iron tools were found in early Native American campsites. There were several French excursions into the Missouri River Valley, but a number of factors kept further development at bay, including run-ins with the Sioux. The first documented European exploration of South Dakota was in 1743 when French explorer Pierre Gaultier de Varennes, Sieur de La Verendrye, may have gotten to within sight of the Black Hills.
In 1763, the French ceded their interests in lands west of the Mississippi to Spain. The Spanish ownership of the lands west of the Mississippi had little impact on the region. In an attempt to oust the British incursions into the area from the north, several excursions were sent upriver from St. Louis to set up a Spanish post near the Mandans in what is now North Dakota. They met with little success. In 1800, Spain ceded the area back to France and in 1803 France sold it to the United States.
Links:
[1] http://www.moon.com/destinations/mt-rushmore-the-black-hills/discover-mount-rushmore-the-black-hills