We report on a study of the superconducting order parameter in Fe(Te1−xSex) thin films (with different Se contents: x = 0.3, 0.4, 0.5) by means of point-contact Andreev-reflection spectroscopy (PCARS). The PCARS spectra show reproducible evidence of multiple structures, namely two clear conductance maxima associated to a superconducting gap of amplitude ∆E ≃ 2.75kBTc and additional shoulders at higher energy that, as we show, are the signature of the strong interaction of charge carriers with a bosonic mode whose characteristic energy coincides with the spin-resonance energy. The details of some PCARS spectra at low energy suggest the presence of a smaller and not easily discernible gap of amplitude ∆H ≃ 1.75kBTc. The existence of this gap and its amplitude are confirmed by PCARS measurements in Fe(Te1−xSex) single crystals. The values of the two gaps ∆E and ∆H, once plotted as a function of the local critical temperature T A c , turn out to be in perfect agreement with the results obtained by various experimental techniques reported in literature.