Is there anything roads-worthy or tourist-unique between the I-10 and I-20 corridors, besides simply driving I-49? I've looked at Natchitoches and Alexandria and come up empty.
From personal experience, take US 71 into Clarence, east at Grayson's BBQ (any day but Monday), and then LA 6 to LA 1 Business through the downtown to Front Street. You can go antique shopping, and then take LA 494 along the Cane River and see some old plantations along with riding the original Jefferson Highway for a portion. DO NOT TAKE LA 1220 TO THE RIVER, since you will get stuck along the dirt road, even with some beautiful sections that are lined with oaks and pecan trees.
You can come into Boyce and Alexandria on LA 1, and take US 71 through Lecompte to Lea's and Bunkie (the last stop before Krotz Springs or Opelousas). Between Bunkie and Baton Rouge or Lafayette, there's nothing to see at all... other than Dr Pepper with cane sugar (the only instance in the state of it being Pepsi-owned) and Mr Pibb.
As far as road-related stuff, you have the Jefferson Highway along US 171 to LA 6 to US 71, along with many abandoned bridges, and Alexandria is home to a 1940's-vintage bypass, with a traffic circle and frontage roads that still exist from around the time of World War II. A modern four-lane highway, with frontage roads, that have culverts dated 1942. It's also the only part of the state which will give you every major metro city on a guide sign (Shreveport, Lafayette, Monroe, Baton Rouge, New Orleans, Lake Charles). Natchitoches has the only cutout outline still on a guide sign for a Louisiana route, other than in Shreveport. It's a boring ride for the most part, though.
Just my $2. I would personally take I-20 to US 165 in Monroe, then take LA 15 between Monroe and Archibald and cross the 1939 Boeuf River Bridge on a beautiful ride from swamps to cotton fields to forested hills. Take US 425 from Archibald to Peck and turn on LA 913 to see a spring where you can still get water from the side of the hill. Then head back east to US 425 in Sicily Island, and take it through Ferriday and Natchez (each home of a KFC all you can eat buffet) and take US 61 south to Baton Rouge and I-10.