There are at least three RV parks between Paris and the Red River. I've not stayed at any of them, because if I hit Paris in the evening, I can get to the other end of the Indian Nation Turnpike, and a selection of Oklahoma CGs, within a couple more hours. Most of my trips through Paris I don't make in the RV, so I stop at a motel.
Depending on your highway coming in, there are a few "parking spot in the field" parks and a state park CG south of Paris. I found the state park CG to be open on weekends only during winter season, but don't know if that means now. For me it was February.
Pat Mayes SP is north on US 271 to Powderly, then west. Cooper Lake SP is south on TX-19 towards Sulphur Springs, turn west on the marked access road before you get to Sulphur Springs. Either lake may also have COE access facilities, but those usually have a shorter season than the state parks.