In recent years, the use of natural flax fibres as a reinforcement in composite building structures has witnessed a growing interest amongst research communities due to their green, economical, and capable mechanical properties. Most of the previous investigations on the load-bearing behaviour of concrete components reinforced with natural flax fibres include inorganic impregnations (or even no impregnation) and exclude the use of textile fabrics. Also, the mechanical behaviour of textiles made of natural flax fibres produced as leno fabrics remains to be investigated. In this paper, the results of tensile tests on concrete components reinforced with bio-based impregnated leno fabrics are presented. For comparison, multilayer non-impregnated and impregnated textiles were considered. The results demonstrated that reinforced textiles yielded an increase in the failure loads compared to the concrete cross-sections without reinforcement. The stress-strain diagrams showed that the curves can be divided into three sections, which are typical for reinforced tensile test specimens. For the impregnated textiles, a narrowly distributed crack pattern was observed. The results showed that impregnated textiles tend to support higher failure stresses with less strains than non-impregnated textiles. Moreover, an increase in the reinforcement ratio alongside larger opening widths of the warp yarns enables higher failure loads.