A process for depositing, with forward progression, graphene on the surface of a metallic or metallized continuous reinforcer, at the periphery of which is positioned a layer of surface metal chosen from copper, nickel and copper/nickel alloys, comprises at least one stage of flame spray pyrolysis (“FSP”), under a reducing atmosphere, of a carbon precursor which generates, in the flame, at least one carbon-based gas such as carbon monoxide which is sprayed onto the surface of the reinforcer in forward progression, and is decomposed thereon to form one or more graphene layers at the surface of the surface metal; an additional stage of graphene functionalization makes it possible to adhere the reinforcer to a polymer matrix such as rubber.