One of the candidate technologies for sixth-generation (6G) wireless communication systems is cell-free massive multiple-input multiple-output (CF-mMIMO) communication, which can control inter-cell interference in MIMO systems. This paper investigates the performance of  a full-duplex (FD) CF-mMIMO system with practical limited-capacity fronthaul links. The proposed system employs a large number $M$ distributed FD access points (APs), arbitrarily distributed $K_d$ downlink (DL) and $K_u$ uplink (UL) half-duplex (HD) single-antenna user equipments (UEs), and a central processing unit (CPU). To exploit energy efficiency (EE) and potential throughput gains of FD systems, each AP is linked to the CPU by a fronthaul link with limited capacity that handles the quantized UL/DL data to and from the CPU. On the same spectrum resource, each AP is expected to support $K$ single-antenna HD UEs, where $K = (K_u + K_d)$. Despite having a minimal signal processing complexity, our approach offers a uniform quality of service (QoS) to all UEs while providing improved spectrum efficiency and EE. Imperfect channel state information and mobility of the UEs are also considered. Closed-form expression for the outage probability is derived using the optimal uniform quantization and maximum-ratio combining/maximum-ratio transmission considering the Welch-Satterthwaite approximation. Additionally, the asymptotic and infinite-$M$ outage performance of the proposed system are analytically studied and verified via Monte-Carlo simulation.