Floyds fork is a scenic river through mostly forested area with many excellent and free access points. Unfortunately, it's hard to catch at a good water level that doesn't involve dragging your boat. You need to pay attention to the USGS gauge when planning a paddle, the river tends to spike very high after a significant rain, then drop very quickly.
Parklands of Floyds Fork
The Parklands of Floyds Fork has a fairly comprehensive guide and maps for paddling Floyds Fork.
American Whitewater also has a brief page describing Floyds Fork.
Green Earth Outdoors Rentals
Green Earth Outdoors offers canoe, kayak, and paddleboard rentals on some sections of Floyds Fork.