According to information available, this line is not officially abandoned (someone please advise). However, the line has not been maintained and is not usable in its current condition. The line is owned by the US Government and is used to serve Fort Bragg via the Aberdeen & Rockfish at Skibo. Apparently any rail traffic comes to the base via CSX now. The line is all but abandoned and makes for some interesting pictures.
UPDATE 02/11/2008: A copy of the abandonment notice for the Cape Fear Railway has been provided by Len Pundt. It is almost 3 MB in size.
An email from Len sheds some more light on these tracks: I happened to read in the local Fayetteville newspaper that the rail line was built during the 1920s by the commander of Fort Bragg as a trolley line in an attempt to tie the Army Post more closely with the town and fend off a round of base closures. I don't recall when the trolley ceased to run.