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Point cloud video transmission is challenging due to high encoding/decoding complexity, high video bitrate, and low latency requirement. Consequently, conventional adaptive streaming methodologies often find themselves unsatisfactory to meet the requirements in threefold: 1) current algorithms reuse existing quality of experience (QoE) definitions while overlooking the unique features of point cloud video thus failing to provide optimal user experience, 2) most deep learning approaches require long-span data collections to learn sufficiently varied network conditions and result in long training periods and capacity occupation, 3) cloud training approaches pose privacy risks caused by leakage of user reported service usage and networking conditions. To overcome the limitations, we present FRAS, the first federated reinforcement learning framework, to the best of our knowledge, for adaptive point cloud video streaming. We define a new QoE model which takes the unique features of point cloud video into account. Each client uses reinforcement learning (RL) to train video quality selection with the objective of optimizing the user's QoE under multiple constraints. Then, a federated learning framework is integrated with the RL algorithm to enhance training performance with privacy preservation. Extensive simulations using real point cloud videos and network traces reveal the superiority of the proposed scheme over baseline schemes. We also implement a prototype that demonstrates the performance of FRAS via real-world tests.