Process for manufacturing a plastic fuel tank equipped with an internal line by molding a parison using a mold comprising two cavities and a core, comprising the following steps: introducing the parison into the mold cavities; introducing the core inside the parison, said core having first been fitted with the line; closing the mold so that the cavities come into leaktight contact with the core; pressing the parison against the cavities by blowing through the core and/or applying a vacuum behind the cavities; fastening the line to the parison over at least two points using a device attached to the core; opening the mold to withdraw the core; and carrying out the final molding of the parison by blow molding and/or thermoforming, in which the line comprises, between its fastening points, a free length that is capable of coming into contact with the parison and/or with an accessory found thereon when the mold is closed, and wherein during the fastening step, at least one intermediate fastening point is created using a device attached to the core.