In this paper we explore the effects of 3.5 MeV proton irradiation on Fe(Se,Te) thin films grown on CaF2. In particular, we carry out an experimental investigation with different irradiation fluences up to 7.30 · 1016 cm-2 and different proton implantation depths, in order to clarify whether and to what extent the critical current is enhanced or suppressed, what are the effects of irradiation on the critical temperature, resistivity, and critical magnetic fields, and finally what is the role played by the substrate in this context. We find that the effect of irradiation on superconducting properties is generally small compared to the case of other iron-based superconductors. The irradiation effect is more evident on the critical current density Jc, while it is minor on the transition temperature Tc, normal state resistivity ρ, and on the upper critical field Hc2 up to the highest fluences explored in this work. In more detail, our analysis shows that when protons implant in the substrate far from the superconducting film, the critical current can be enhanced up to 50% of the pristine value at 7 T and 12 K; meanwhile, there is no appreciable effect on critical temperature and critical fields together with a slight decrease in resistivity. On the contrary, when the implantation layer is closer to the film-substrate interface, both critical current and temperature show a decrease accompanied by an enhancement of the resistivity and lattice strain. This result evidences that possible modifications induced by irradiation in the substrate may affect the superconducting properties of the film via lattice strain. The robustness of the Fe(Se,Te) system to irradiation-induced damage makes it a promising compound for the fabrication of magnets in high-energy accelerators.