The invention relates to a reinforced product, usable in particular for the reinforcement of a finished rubber article, comprising one or more textile or metallic reinforcement yarns covered with a sheath comprising a thermoplastic polymeric composition, said sheathed yarn(s) being in turn embedded in a rubber composition referred to as coating rubber, characterised in that the coating rubber is a composition containing at least one diene rubber, a reinforcing filler and a sulphur vulcanisation system which comprises a vulcanisation accelerator having a vulcanisation start time, referred to as t0, of less than 3.5 minutes, and preferably of not more than 3 minutes.