The optical responses of semiconducting transition metal dichalcogenides are dominated by excitons. Being able to strongly interact with light and other materials excitations, excitons in semiconductors are prototypes for investigating many-particle and strong-field physics, including exciton-exciton, exciton-photon, and exciton-phonon interactions. Strong exciton-photon interactions, in particular, can lead to the emergence of exciton-polariton hybrid quasiparticles with peculiar characteristics, and a tendency toward macroscopic and spontaneous coherence. Normally, far-field and near-field optical spectroscopy techniques are used to investigate exciton-photon interactions. Here, we demonstrate that the radiation generated by moving electrons in transition metal dichalcogenides, namely Cherenkov radiation, can strongly interact with excitons. We investigate the coherence properties and spectral signatures of exciton-photon interactions in TMDC bulk crystals, using cathodoluminescence spectroscopy. Our findings lay the ground for cathodoluminescence spectroscopy and in particular electron-beam techniques as probes of exciton-polariton spontaneous coherence in semiconductors, beyond the well-known plasmonic investigations.