Phase-pure cuprous oxide (Cu2O) thin films doped with Fluorine (F) have been prepared under thermal diffusion at diffusion temperatures of 1123 K and 1223 K and it is found that higher diffusion temperature leads to larger grain size. F-doping slightly reduces the lattice constant and F-doped Cu2O thin films exhibit p-type semiconductor characteristics. The reduction of band gap occurs due to F-doping induced impurity band, because F-doped samples have larger Urbach tails than that of undoped samples. Theoretical calculation demonstrates that substitutional F-doping makes Cu2O almost metallic because the energy bands of F atoms enter the forbidden gap, and interstitial F-doping narrows the band gap because F atoms contribute to the valence bands. The doped F atoms are very possibly interstial and play the role of acceptors in Cu2O. Phase-pure Cu2O doped with F have smaller resistivity and larger hole concentration, implying potential application in solar cells.