Ion irradiation of superconductors allows both the establishment of their radiation hardness and the modification and optimization of their properties useful for applications. In this work, we investigate the effects of proton irradiation with different energies on Fe(Se,Te) thin films grown on CaF$_2$ and on buffered YSZ substrates. These systems allowed us to perform preliminary studies for the development of Fe(Se,Te) coated conductors. Critical temperature and critical current were measured for different levels of displacement damage, and with ion implantation happening at various depths inside the substrate, as evaluated by simulations with Monte Carlo codes. All measurements evidenced that these Fe(Se,Te) films are robust against proton induced damage, and that an increase of critical current can be achieved introducing pointlike defects in the superconductor. However, we find that damage induced in the substrate also plays a crucial role in modifying superconducting film properties through a variation of the strain exerted on the film. This strain degrades superconducting parameters and should be minimized.