Many applications, e.g., in shared mobility, require coordinating a large number of agents. Mean-field reinforcement learning addresses the resulting scalability challenge by optimizing the policy of a representative agent. In this paper, we address an important generalization where there exist global constraints on the distribution of agents (e.g., requiring capacity constraints or minimum coverage requirements to be met). We propose Safe-M3-UCRL, the first model-based algorithm that attains safe policies even in the case of unknown transition dynamics. As a key ingredient, it uses epistemic uncertainty in the transition model within a log-barrier approach to ensure pessimistic constraints satisfaction with high probability. We showcase Safe-M3-UCRL on the vehicle repositioning problem faced by many shared mobility operators and evaluate its performance through simulations built on Shenzhen taxi trajectory data. Our algorithm effectively meets the demand in critical areas while ensuring service accessibility in regions with low demand.