In this work, we analyze the downlink performance of a cell-free massive multiple-input-multiple-output system with finite capacity fronthaul links between the centralized baseband units and the access point (APs). Conditioned on the user and AP locations, we first derive an achievable rate for a randomly selected user in the network that captures the effect of finite fronthaul capacity. Further, we present the performance analysis for two different types of network architecture, namely the traditional and the user-centric. For the traditional architecture, where each user is served by all the APs in the network, we derive the user rate coverage using statistical properties of the binomial point process. For the user-centric architecture, where each user is served by a specified number of its nearest APs, we derive the rate coverage for the typical user using statistical properties of the Poisson point process. In addition, we statistically characterize the number of users per AP that is necessary for coverage analysis. From the system analyses, we conclude that for the traditional architecture the average system sum-rate is a quasi-concave function of the number of users. Further, for the user-centric architecture, there exists an optimal number of serving APs that maximizes the average user rate.