A low band-gap copolymer PDTBTFV alternating bis-thienyl-(bis-alkoxy)-benzothiadiazole blocks with difluorovinylene units and its non-fluorinated counterpart PDTBTV have been synthesized and characterized as donor materials in bulk heterojunction (BHJ) solar cells with PCBM as the acceptor. The solar cells with the fluorinated polymer show better photovoltaic performances than those recorded with the non-fluorinated material. Comparative spectroscopic and computational studies, together with morphological, electrical and optical characterization of thin films, have been carried out to shed light on the reasons for the improvement of performances as induced by the double bond fluorination. Our study introduces the fluorinated double bond as a new conjugated unit in donor polymers for BHJ solar cells.