The cellular Vehicle-to-Everything (C-V2X) radio access technology, specified by the Third Generation Partnership Project (3GPP), enables direct communications between vehicles, using the sidelink radio resources over the PC5 interface. In C-V2X Mode 4, a vehicle autonomously selects the resources and keeps them for consecutive transmissions before a resource reselection is triggered, according to a sensing-based semi-persistent scheduling mechanism. A wrong estimation of the resource occupancy status may lead to persistent packet losses, due to collisions with simultaneous transmissions from other vehicles. In this paper, we propose to provide vehicles with on-board full-duplex transceivers and harness this capability (i) to make the sensing phase more accurate, (ii) to make a more informed resource reselection decision, and (iii) to enhance packet decoding while transmitting. Achieved simulation results show that the proposal provides several improvements in terms of packet transmission reliability and timeliness when compared against the legacy C-V2X Mode 4.