Fiber Reinforced Cementitious Matrix (FRCM) systems are increasingly used for the structural strengthening of masonry buildings. These systems typically incorporate composite grids—commonly made from carbon, basalt, glass, or aramid fibers—embedded in inorganic matrices. In the pursuit of more environmentally sustainable alternatives, natural fibers are emerging as a promising option. This study presents a preliminary investigation into the use of flax fibers within FRCM systems, focusing on their mechanical behavior through tensile testing of both flax yarns and grids. The specimens, extracted from a roll composed of flax fibers impregnated with biopolymers forming a balanced mesh, were manufactured and tested at the Olympus Srl laboratory in accordance with Italian FRCM standards. Tensile tests were performed under displacement-controlled conditions, and the results are presented as stress–displacement curves. From these, the maximum tensile stress and average values for each specimen type were determined. Future research will include tensile testing of the same flax fiber grids embedded in natural hydraulic lime mortar.