A thin packaging film 1 includes a reference area 2 having a closed contour and which is surrounded over its entire periphery by a tear-off area, an incipient tear 3 being precut in this film so as to intercept this contour while leading into the latter while forming a gripping portion 4 capable of being pulled away from the plane of this thin film, the reference area being designed so as to trap one end of this incipient tear within the contour while the other end propagates by tearing in a spiral from the tear-off area over at least 180° around this reference area when the gripping portion begins to undergo pulling. This closed contour is preferably circular. The closed contour area can in particular be an opening, or a portion of film surrounded by a reinforcement material loop.