We present Raman spectroscopic studies of the isostructural and isoelectronic Eu_6−xSr_xC₆₀ (x = 0, 3, 5, 6) and Ba₆C₆₀ compounds. The Raman spectra of the Eu-based fullerides show dramatic changes compared to the pure alkaline-earth systems, including significant broadening, splitting and frequency shifts of the fivefold degenerate H_g intramolecular modes of C₆₀. Moreover, the A_g(2) mode exhibits an even larger downshift and a remarkable broadening. These findings are consistent with distortions of the C₆₀ molecular cages and a considerable electron-phonon coupling strength—strongly enhanced in the Eu containing systems—originating from the strong orbital hybridization between the metal atom and the C₆₀ molecule.