Process for manufacturing a plastic fuel tank (FT) equipped with an internal accessory, by molding a parison using a mold comprising two cavities and a core, said process comprising the following steps: the parison is introduced into the mold cavities; the core is introduced inside the parison, the core having first been fitted with the accessory; the mold is closed so that the cavities come into leaktight contact with the core; the parison is pressed against the cavities by blowing through the core and/or applying a vacuum behind the cavities; the accessory is fastened to the parison by snap riveting using a device attached to the core; the mold is opened to withdraw the core; and the final molding of the parison is carried out by blow molding and/or thermoforming. The accessory comprises an orifice for the snap riveting and at least one protuberance which, during the fastening of the accessory by snap riveting, will at least partially melt to form a local weld which is at another location than the obtained rivet to obtain two different attachment points.