We investigate the origin of large magnetocapacitive effects in CdCr ₂S₄ single crystals focusing on phonon anomalies in the fluctuation regime T < T* = 130 K and with the onset of ferromagnetic order T_c = 84.4 K. The observation of longitudinal optical and formerly infrared active modes for T < T_c is used to propose a loss of inversion symmetry and Cr off-centering. Further anomalies in intensity, frequency, and linewidth have an onset temperature T* that coincides with the onset of magnetocapacitive effects. The respective intensity anomalies are attributed in part to an enhanced electronic polarizability of displacements that modulate the Cr-S distance and respective hybridization. This is taken as a prerequisite to the proposed Cr off-centering. Anomalies due to the previously disregarded photodoping and resonance are analyzed comparing different excitation energies.