Process for the manufacture of a component comprising a stack of a functional layer on a composite film, the composite film comprising a matrix made of thermoplastic polymer inside which are dispersed particles (24; 146) conferring, on this composite film, physical properties essential to the operation of the component, the exodiameter of the particles being between 1 nm and 100 μm and the volume of the particles inside the composite film representing more than 1% of the volume of this composite film, this process comprising: a) the deposition of the composite film (8; 134) directly on a rigid substrate (6; 142, 138, 140), the thickness of which is strictly greater than the thickness of the film, the composite film then exhibiting an external face turned the opposite way from the substrate, at this stage, the temperature of the composite film being less than its glass transition temperature, so that this film is referred to as "hard", then b) the deposition of the functional layer (10; 174) directly on the external face of the composite film, characterized in that, between stages a) and b), the process comprises: 1) the heating of the composite film (8; 134) in order for its temperature to exceed the glass transition temperature of its matrix, so as to soften it, 2) when the composite film (8; 134) is softened, the flattening of the external face of the composite film by a smooth face (20; 120) resting directly over the whole of this external face, this smooth face forming part of the front face of a flexible membrane (48; 110), the whole of the rear face of which, located on the side opposite the front face, is pushed against the composite film by a fluid, then 3) the cooling of the composite film below the glass transition temperature in order to again harden it, then 4) the withdrawal of the membrane (48; 110) in order to mechanically separate its front face from the external face of the composite film. a) the deposition of the composite film (8; 134) directly on a rigid substrate (6; 142, 138, 140), the thickness of which is strictly greater than the thickness of the film, the composite film then exhibiting an external face turned the opposite way from the substrate, at this stage, the temperature of the composite film being less than its glass transition temperature, so that this film is referred to as "hard", then b) the deposition of the functional layer (10; 174) directly on the external face of the composite film, 1) the heating of the composite film (8; 134) in order for its temperature to exceed the glass transition temperature of its matrix, so as to soften it, 2) when the composite film (8; 134) is softened, the flattening of the external face of the composite film by a smooth face (20; 120) resting directly over the whole of this external face, this smooth face forming part of the front face of a flexible membrane (48; 110), the whole of the rear face of which, located on the side opposite the front face, is pushed against the composite film by a fluid, then 3) the cooling of the composite film below the glass transition temperature in order to again harden it, then 4) the withdrawal of the membrane (48; 110) in order to mechanically separate its front face from the external face of the composite film.