This paper analyzes the spectral/energy efficiency (SE/EE) of a full-duplex (FD) cell-free (CF) massive multiple-input multiple-output (mMIMO) over Rician fading channels. Due to the FD radios, the access points (APs) suffer from self-interference (SI) and inter-AP interference (IAI) while the downlink (DL) users’ signals are corrupted by the uplink (UL) users’ transmissions. We consider the case, where low-resolution analog-to-digital converters (ADCs) are utilized at the APs and DL users, which introduces the quantization noise (QN). The combined effects of Rician κ-factor, residual SI/IAI, UL-to-DL interference, multi-user interference, and QN on the UL/DL SEs are characterized. The UL SE is degraded by the increase in DL power, whereas the growth in UL power deteriorates the DL SE. The effects of the residual SI/IAI and UL-to-DL interference are worsened by the low-resolution ADCs. We optimize the UL/DL transmit powers to maximize the overall sum SE of the network. It is observed that the proposed power allocation algorithm brings substantial sum SE gain. A trade-off analysis between the EE and SE, as a function of the ADCs’ resolution, shows that the entire envelope of the operating region of FD CF mMIMO is enhanced in Rician channels.