Methanol vapor permeability and pore formation features in stretched polytetrafluoroethylene (PTFE) films used as a precursor of composite cation-exchange membranes have been studied. Porous structures of the precursor have been formed via stretching PTFE films in air, toluene, isopropyl alcohol, and CCl4. Permeability has been determined according to the evaporation of a liquid through a porous film; porosity, according to the increase in the film volume during stretching; pore formation features, according to optical microscopy images of porous films and their transverse microsections. It has been found that, with an increase in the stretch ratio, the porosity of PTFE films increases almost linearly, while the methanol vapor permeability increases exponentially. The permeability of the films stretched in liquids is 20 times higher than the permeability of the films stretched in air at comparable stretch ratio and porosity values. The considerably higher permeability of the films stretched in liquids and the observed differences in their porous structure suggest that the liquids are actively involved in the formation of through pores in the direction connecting the film surfaces, i.e., in the direction that determines the transport and conductive properties of composite membranes based on stretched PTFE films.