Multipartite entangled states are an essential building block for advanced quantum networking applications. Realizing such tasks in practice puts stringent requirements on the characteristics of the states in terms of fidelity and generation rate, along with a desired compatibility with telecommunication network deployment. Here, we demonstrate a photonic platform design capable of producing high-fidelity Greenberger-Horne-Zeilinger (GHZ) states, at telecom wavelength and in a compact and scalable configuration. Our source relies on spontaneous parametric down-conversion in a layered Sagnac interferometer, which only requires a single nonlinear crystal. This enables the generation of highly indistinguishable photon pairs, leading by entanglement fusion to four-qubit polarization-entangled GHZ states with fidelity up to $(94.73 \pm 0.21)\%$ with respect to the ideal state, at a rate of 1.7Hz. We provide a complete characterization of our source and highlight its suitability for practical quantum network applications.