Thin packaging film (1, 1′, 11, 11′) comprising a reference area (2, 2′, 12, 12′) having a closed contour and being surrounded over its entire periphery by a tear-off area, an incipient tear (3, 3′, 13, 13′) being precut in this film so as to intercept this contour, leading into the latter while forming a gripping portion (4, 4′, 14, 14′) capable of being pulled away from the plane of this thin film, said reference area being designed so as to trap one end of this incipient tear within said contour while the other end propagates (3A, 3A′, 13A, 13A′) 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 such pulling.