On the path to zero fatalities on the roadways, all vehicles have to periodically broadcast cooperative awareness messages (CAMs) in a timely and reliable manner, even in areas of high traffic density. The carrier senses multiple access with collision avoidance (CSMA/CA) scheme of IEEE 802.11, the de-facto standard for vehicular communications, is known to offer no reliability to broadcast packets that cannot be acknowledged, and to poorly perform at high network load due to collisions and interference. In this paper, an enhanced CSMA/CA protocol is analyzed for vehicular networks, which improves the CAM timeliness and reliability by leveraging full-duplex (FD) transceivers on board. FD devices can listen to the channel while transmitting, thus making collision detection viable. A FD vehicle can detect a CAM collision while sending, promptly abort the packet and retransmit it later. Results achieved through an analytical model under mathematically tractable assumptions, and through extensive system-level simulations in a complex urban environment, show the effectiveness of the protocol to cope with direct collisions, especially in high traffic areas, paving the way towards the realization of cooperative automated driving.