Falling trees or their limbs can cause power lines to break or sag, sometimes resulting in devastating wildfires. Conventional protections such as circuit breakers, overcurrent relays and automatic circuit reclosers may clear short circuits caused by tree contact, but they may not detect cases where the conductors remain intact or a conducting path is not sufficient to create a full short circuit. In this paper, we introduce a novel, non-intrusive monitoring technique that detects and locates fallen trees, even if a short circuit is not triggered. This method employs distributed fiber optic sensing (DFOS) to detect vibrations along the power distribution line where corresponding fiber cables are installed. A physics-informed ResNet model is then utilized to interpret this information and accurately locate fallen trees, which sets it apart from traditional black-box predictions of machine learning algorithms. Our real-scale lab tests demonstrate highly accurate and reliable fallen tree detection and localization.