Entanglement is a universal resource in quantum networks, yet entangled photon sources are typically custom-made for a specific use case. Versatility, both in terms of state modulation and tunability of the temporal properties of the photons, is the key to flexible network architectures and cryptographic primitives that go beyond quantum key distribution. Here, we report on a flexible source design that produces high-quality entanglement in continuous-wave and GHz-rate-pulsed operation modes. Utilizing off-the-shelf optical components, our approach uses a fiber-based Sagnac loop to generate polarization-entangled photons at telecom wavelength with high efficiency and fidelities above 0.99. Phase modulation up to GHz before entangled state generation is also possible for fast entangled state switching. We show phase modulation at 100 MHz with an average fidelity of 0.95. Furthermore, the source 60 nm spectral bandwidth is entirely compatible with fully reconfigurable wavelength-multiplexed quantum networks.