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The energetic proximity of phonons and crystal-electric-field (CEF) levels in rare earth materials is conducive to strong electron-phonon coupling that can give rise to interesting phenomena and novel material properties, including Davydov splittings, cooperative Jahn-Teller effects, and hybrid vibronic exctiations. To explore the role that CEF-phonon coupling plays in governing the physical properties of one class of rare earth materials, the rare earth sesquioxides, we present Raman spectroscopic measurements of C-type Eu₂O₃ as a function of temperature. It has been previously reported that near room temperature, energy transfer can readily occur between two symmetry inequivalent Eu³⁺ ions in Eu₂O₃ [1] mediated by electron-phonon interactions. Our Raman spectra reveal features with strongly temperature-dependent intensities that energetically coincide with Raman-forbidden T_u phonons predicted by lattice dynamics calculations [2] and the energy differences between excited states of the C₂ and S₆ Eu³⁺ ions of Eu₂O₃ [1]. We propose that the Raman selection rules for these excitations are relaxed by the strong electron-phonon coupling present in Eu₂O₃.