I present to you one of my favorite maps of the Red River via Nicolas de Fer's illustrated map, using descriptions collected from the Jesuits, published in France in 1718.
The red road that you see is identified as the "Route de Mr. de la Salle." Well, not really. René-Robert Cavelier, Sieur de La Salle was a semi-successful colonizer who brought a few hundred French people to what he believed was the mouth of the Mississippi River in 1684. Instead, he and his ship, the Belle, landed near where the Colorado River of Texas empties into the Gulf of Mexico. The Belle, anchored off-shore, sunk in a storm, and the French were stranded. Now, thoroughly lost, La Salle searched for the actual Mississippi River for two years before he was killed by his own men in a mutiny. You'd think he would have asked for directions.
The party that was loyal to him undertook the journey to the Mississippi River instead, traversing the Red River at the Caddo Villages in today's extreme northeastern Texas and southwestern Arkansas. This expedition was led by Henri Joutel, the mission's second-in-command who still gave all credit to his dead boss, which is why the road is explained as La Salle's route.
Another note of interest is that the Red River is called the Riviere de Marne on this map. This might have been a name given to its similarity to the Marne River in France, or may have been named for a French politician — for example, the Mississippi River was once named the Riviere Colbert in French maps to honor the king's finance minister who funded expeditions.
Other things I like about the map: the turkeys, the salamander (alligator? Remember that Nicolas de Fer didn't know what they looked like) and the clumsy looking cows/elks. Also, Natchitoches is surrounded by native villages; at this point, the settlement was only four years old!
The full map is for sale as an original copy at Barry Lawrence Ruderman.