Suitably equipped with cameras and sensors, uncrewed aerial vehicles (UAVs) can be instrumental for wildfire prediction, tracking, and monitoring, provided that uninterrupted connectivity can be guaranteed even if some of the ground access points (APs) are damaged by the fire itself. A cell-free network structure, with UAVs connecting to a multiplicity of APs, is therefore ideal in terms of resilience. This work proposes a trajectory optimization framework for a UAV swarm tracking a wildfire while maintaining cell-free connectivity with ground APs. Such optimization entails a constant repositioning of the multiplicity of UAVs as the fire evolves to ensure that the best possible view is acquired and transmitted reliably, while respecting altitude limits, avoiding collisions, and proceeding to recharge batteries as needed. Given the complexity and time-varying nature of this multi-UAV trajectory optimization, reinforcement learning is leveraged, specifically the twin-delayed deep deterministic policy gradient algorithm. The approach is shown to be highly effective for wildfire tracking and coverage and could be likewise applicable to survey other natural and man-made phenomena, including weather events, earthquakes, or chemical spills.