Can anyone tell me if there are any bus lines or car service or anything from Paris, TN to Nashville, TN.
The only public transit service available is a flexible route service. It is the type of thing that is only available to seniors and those with disabilities in some cities, but there they offer to everyone.
They have a very limited operation, and the center of the web page says it is $25 round trip to the Nashville area.
There may also be some Greyhound routes, unless you found that not to be the case, glabah.
They have Paris, Ontario and Paris, Texas in their database, but not Paris, Tenn. There might be something somewhat close, but since Greyhound doesn't make its route map easily available it is difficult to know what goes where. The only choice you have is to put in city pairs and see what happens.