You may not like doing it, but when you order an item at a distance – by phone or online – and it arrives damaged, the firm that supplied it is deemed legally responsible, says the official consumer rights agency, the Institut National de la Consommation.
If the item arrives damaged, then the supplier should replace it, at their own cost, or reimburse you. It is up to the sender, in turn, to take action against the transporters.
As proof, it is recommended that you do not simply sign off the bon de livraison form that the transporter asks you to sign but that you refuse the damaged goods and write on the form the reason, such as je refuse d’accepter la livraison – colis endommagé (I refuse to accept delivery – damaged parcel).
You should not have to pay any additional delivery costs linked to this.
It is recommended that, as soon as possible, you send the supplier a recorded delivery letter (lettre recommandée avec avis de réception) putting the firm on notice to supply an undamaged item, with wording including the phrase je vous mets en demeure de…. (I put you on legal notice to…).