A flexible envelope having a body initially scaled at one end in a zone designed to be opened, the body including at least two walls (26A, 26B) whereof the longitudinal edges are bound together along a longitudinal weld (14) extending over the height of the body, at least one of the walls (26A, 26B) extending outside the body beyond the longitudinal weld (14) to form a flap (36). The package has a weakened line (42) constituting an incipient tear formed on the flap (36) along the longitudinal weld (14), the weakened line (42) delimiting on the flap (36) a strip (43A) at least locally detachable from the package body and an adhesive (44) borne by a strip (43A), the adhesive (44) being designed to enable the strip to be subsequently bonded against the package outer surface.