I would stay away from the river until the flood danger passes. I would take
I-530 south to Pine Bluff, US65 south (east) to US425 south to Natchez MS. We stay at the River View RV Resort in Vidalia LA but I would call the morning of the day you arrive to make sure it's the rv park is not flooded. The reports say that in Vidalia the river will possibly crest about Jan 18th. Nearby is the Frogmore Cotton Gin and Plantation in Ferriday LA. From Natchez MS, take US61 east to US98 to Hattiesburg MS. Take I-59 back to US98 east then take I-55 south to I-12 to I-10. Fountainbleu State Park in LA off I-12 is a good stop. It's about a 45 minute drive into New Orleans from there. Or we like to stay at Lakeside RV Park in Livingston LA. You can also drive into New Orleans from there. If you stop in New Orleans, don't miss the World War II Museum.