A reinforced product (21) comprises: an elastomer matrix (23), several reinforcing elements (44) embedded in the elastomer matrix (23), the reinforcing elements (44) being arranged side by side in a main direction (X1), Each reinforcing element (44) comprises: several filamentary elements (46), and at least one communal sheath collectively coating the filamentary elements (46) and comprising at least one layer of a thermoplastic polymer composition. The ratio R1=ODO/E of the mean minimum thickness ODO of elastomer present on the back of the sheath to the mean thickness E of the reinforced product (21) is less than or equal to 0.17, the mean minimum thickness of elastomer ODO and mean thickness E of the reinforced product (21) being measured in a direction substantially perpendicular to the main direction (X1).