The gas permeability of equilibrium foam films stabilized with an alpha-olefin sulfonate surfactant was measured. The permeability coefficient, K (cm/s), was obtained as a function of the electrolyte (NaCl) concentration, surfactant concentration, and temperature. The addition of salt to the film-forming solution leads to a decrease of the film thickness, which was complemented by an increase of K up to a certain value. Above that critical salt concentration, the gas permeability decreases even though the film thickness also decreases. We explain this effect as a result of interplay of the film thickness and the adsorption monolayer permeability for the permeability of the whole film, i.e., the thermodynamic state of the film. The classical theories that explain the process were applied. The gas permeability of the film showed an unexpected increase at surfactant concentrations well above the critical micelle concentration. The origin of this effect remains unclear and requires further studies to be clarified. The experiments at different temperatures allowed the energy barrier of the permeability process to be estimated.