Quantum information, communication, and sensing rely on the generation and control of quantum correlations in complementary degrees of freedom. Free electrons coupled to photonics promise novel hybrid quantum technologies, although single-particle correlations and entanglement have yet to be shown. In this work, we demonstrate the preparation of electron-photon pair states using the phase-matched interaction of free electrons with the evanescent vacuum field of a photonic chip-based optical microresonator. Spontaneous inelastic scattering produces intracavity photons coincident with energy-shifted electrons, which we employ for noise-suppressed optical mode imaging. This parametric pair-state preparation will underpin the future development of free-electron quantum optics, providing a route to quantum-enhanced imaging, electron-photon entanglement, and heralded single-electron and Fock-state photon sources.