In this paper, we integrate device-to-device (D2D) communications with coordinated multi-point (CoMP) in downlink cloud radio access network (C-RAN), targeting at using the proximity nature of D2D communications to improve system spectral efficiency. In particular, using stochastic geometry, we first derive the signal-to-interference ratio (SIR) distribution at a typical downlink user and a typical D2D receiver, considering zero-forcing beamforming (ZFBF) as the CoMP scheme. Based on the results, we analyze the effect of D2D communications on enhancing the area spectral efficiency (ASE) of the CoMP enabled C-RAN system. Numerical results show that increasing the cooperative cluster size would potentially degrade the system ASE when the network is heavily loaded. Furthermore, it is observed that the addition of D2D links, despite introducing excessive cross-tier interference to downlink users, can provide significant gains if properly designed.