The fluorinated boron nitride (F-BN) nanostructures are found to be fully spin polarized and half-metallic by means of first-principles calculations based on the Heyd-Scuseria-Ernzerhof hybrid functional. It is found that the full spin polarization and 1 μB local moment in F-BN nanotubes are independent of tube radius and it is also robust in planar ribbons and sheets. The long-ranged ferromagnetic coupling between local moments decreases with decreasing tube radius. This suggests that F-BN systems with small local curvatures could be more easily experimentally observed and have greater potential applications in spin devices.