We observe charge-order fluctuations in the quasi-two-dimensional organic superconductor β′′-(BEDT-TTF)2SF5CH2CF2SO3, both by means of vibrational spectroscopy, locally probing the fluctuating charge order, and by investigating the in-plane dynamical response by infrared reflectance spectroscopy. The decrease of the effective electronic interaction in an isostructural metal suppresses both charge-order fluctuations and superconductivity, pointing to their interplay. We compare the results of our experiments with calculations on the extended Hubbard model.