Recently, Unmanned Aerial Vehicles (UAVs) have attracted the attention of researchers in academia and industry for providing wireless services to ground users in diverse scenarios like festivals, large sporting events, natural and man-made disasters due to their advantages in terms of versatility and maneuverability. However, the limited resources of UAVs (e.g., energy budget and different service requirements) can pose challenges for adopting UAVs for such applications. Our system model considers a UAV swarm that navigates an area, providing wireless communication to ground users with RIS support to improve the coverage of the UAVs. In this work, we introduce an optimization model with the aim of maximizing the throughput and UAVs coverage through optimal path planning of UAVs and multi-RIS phase configurations. The formulated optimization is challenging to solve using standard linear programming techniques, limiting its applicability in real-time decision-making. Therefore, we introduce a two-step solution using deep reinforcement learning and particle swarm optimization. We conduct extensive simulations and compare our approach to two competitive solutions presented in the recent literature. Our simulation results demonstrate that our adopted approach is 20 \% better than the brute-force approach and 30\% better than the baseline solution in terms of QoS.