A cold-rolled sheet is provided. The cold-rolled sheet includes a steel substrate with a carbon content C0 between 0.07% and 0.5%, expressed by weight, and a metal pre-coating on at least the two principal faces of the steel substrate. The substrate has a decarburized area on the surface of each of the two principal faces. The depth p50% of the decarburized area is between 6 and 30 micrometers, and p50% is the depth at which the carbon content is equal to 50% of the content C0. The sheet does not contain a layer of iron oxide between the substrate and the metal pre-coating.