The interaction between photogenerated carriers with lattice vibrations plays a fundamental role in the nonradiative recombination and charge-transfer processes occurring in photocatalysis and photovoltaics. Here, we employ Raman spectroscopy to investigate the electron-phonon interaction in ternary layered Cu2MoS4 nanoflakes. Multiphonon Raman scattering with up to fourth-order longitudinal optical (LO) overtones is observed under above-band gap excitation, indicating a strong electron-phonon coupling (EPC) that could be described by the cascade model. The Huang-Rhys factor was derived to characterize the strength of EPC and was found to be increasing with decreasing temperature. First-principles calculations of lattice dynamics and electron-phonon matrix elements suggest that the strong EPC in Cu2MoS4 is dominated by Fröhlich coupling between electron and the electric fields, which is induced by the localized phonon mode originating from a flat phonon branch. Our findings facilitate the understanding of electron-phonon interaction in 2D ternary Cu2MoS4 and pave the way for developing and optimizing optoelectronic devices.