Effective file transfer is fundamental to many applications in highway Vehicular Ad Hoc Networks (VANETs), e.g., social network applications, advertisement distributions, road traffic report, etc. However, due to the sparse development of roadside units (or access points) and the limited connection time between fast-moving vehicles, file transfer is susceptible to frequent interruptions, and accordingly resulting in incomplete file transfers. The incomplete file transfer leads to not only poor user performance with application playback failures, but also a colossal waste of bandwidth. To tackle this issue, in this paper, we consider a bi-directional highway vehicular network scenario where request vehicle and source vehicle are in the opposite direction, and propose a fuzzy logic-based cooperative file transfer scheme (FL-CFT). With the proposed scheme, the request file can be transferred completely from the source vehicle to request vehicle through multiple relay cluster members. As for the selection of relays, in general, finding an optimal relay subject to multiple constrains is an NP-complete problem that cannot be exactly solved in polynomial time. Accordingly, a fuzzy logic approach is utilized to optimally selects relays to help transfer the file and ensure the file integrity, which considers the relative velocity, distance, and predicted connection time among vehicles. The proposed scheme is self-organized and fully distributed, which does not require any assistance from roadside units (or access points). Simulation results show that FL-CFT outperforms the state-of-the-art file transfer schemes in file integrity on highway VANETs.