A fluid dispensing device including a cap having an insertion orifice and a stopper, the cap and the stopper being arranged so that the stopper is mounted in the cap on the side of the insertion orifice. The device includes a deformable chamber whose interior volume is arranged to contain a fluid, the chamber having an inlet to conduct a fluid along a circulation path of fluid from the inlet then through the chamber and to an outlet. The device further includes a pressing part arranged to be movable so as to modify the interior volume, and at least one reservoir film extending towards outside of the cap to form a fluid reservoir in communication with the chamber through the inlet, the at least one reservoir film being held by a force exerted by the stopper on the cap.