The invention relates to a molding and fitting system (100) for a first part and a second part, including: two guide rails (102); a carriage (108) translatably movable on the guide rail (102); a series of first recesses (120); a maneuvering gear mounted on the carriage (108) and rotatably movable about an axis perpendicular to the movement direction of the carriages (108); a series of second recesses (116) mounted so as to be capable of moving between a lower position and an upper position; a rack adapted so as to move in parallel with the guide rail (102) and for meshing with the moving gears of the carriage (108); a locking device (106) adapted for alternately locking said carriage (108) with the rack and the guide rail; and an actuation device (04) for moving the rack.