This element includes a plurality of longitudinal carbon fiber filaments (52) and a polymeric matrix (50) receiving the filaments (52) for binding them together, the matrix (50) forming a ribbon intended to be wound around a longitudinal body of the flexible line. The armor element (42) includes at least one optical fiber (54) received in the matrix (50), the optical fiber (54) having an elongation at break of more than 2%, as measured with the ASTM-D 885-03 standard.