To provide a process for producing a film excellent in water vapor barrier property, tensile elongations, and transparency. A resin material containing polychlorotrifluoroethylene (PCTFE) is melted and extruded into a film from an extrusion die, the extruded product is brought into contact with a cooling roll having a surface temperature of at most 120° C. in a state such that the surface temperature of the extruded product is higher than the crystallization temperature of PCTFE to form a film web, and the film web is subjected to heat treatment at from 80 to 200° C. to obtain a film.