The development of prototype metropolitan-scale quantum networks is underway and entails transmitting quantum information via single photons through deployed optical fibers spanning several tens of kilometers. The major challenges in building metropolitan-scale quantum networks are compensation of polarization mode dispersion, high-precision clock synchronization, and compensation for cumulative transmission time fluctuations. One approach addressing these challenges is to co-propagate classical probe signals in the same fiber as the quantum signal. Thus, both signals experience the same conditions, and the changes of the fiber can therefore be monitored and compensated. Here, we demonstrate the distribution of polarization entangled quantum signals co-propagating with the White Rabbit Precision Time Protocol (WR-PTP) classical signals in the same single-core fiber strand at metropolitan-scale distances. Our results demonstrate the feasibility of this quantum-classical coexistence by achieving high-fidelity entanglement distribution between nodes separated by 100 km of optical fiber. This advancement is a significant step towards the practical implementation of robust and efficient metropolitan-scale quantum networks.