Providing seamless connectivity during transit in vehicular ad hoc networks (VANETs) is the most promising and challenging task. In VANET, the vehicles are able to communicate with other vehicles and also with the infrastructure units such as road side unit (RSU). The coverage range of RSU is not sufficient to cover the whole road. The vehicle can drive to an area which is not covered by any of the RSUs, and it is termed as congested zone (CZ). This will extremely lead to traffic congestion and maximize blocking probability. In order to provide connectivity between the road segments and to avoid long delay in message transmission, unmanned aerial vehicles (UAVs) are placed in CZs, which act as relay nodes. To enhance the connectivity of the vehicles, a fuzzy-based UAV-assisted handoff scheme (F-UAV-HO) is proposed in this work. By adopting fuzzy, the unwanted participation of UAV is limited in non-congested traffic, thereby saving the battery resource. To validate the proposed work, the simulations are executed in Network Simulator 2.35. The proposed system outperforms other conventional UAV-assisted schemes in congested traffic in terms of average end-to-end delay, PDR and throughput.