This paper evaluated the structural behavior of shear-strengthened externally bonded FRCM composites. The additional shear strength of FRCM composites with three different types of textile grids (T1, T2, and T3) was analyzed for different crack patterns and failure modes. The influence of the internal transverse reinforcement ratio (ρw: 0.19%, 0.285%) and application method (SB: side bonding; UW: U-type wrapping) on the FRCM-strengthened beam was investigated. Furthermore, the interaction of FRCM composites with internal shear reinforcement was analyzed based on the strain distributions measured in the experiments. The experimental results showed that the failure modes (flexural, shear slippage, and shear debonding) changed depending on the type of textile grid applied. A reduction in shear reinforcement strain (interaction) due to FRCM strengthening was observed for all the strengthened beams, with differences depending on the shear reinforcement ratio and the type of textile grid. In addition, the ratio of the strain measured at the ultimate load to the strain of the textile grid in shear-failed reinforced beams was the lowest for the T3 grid, which had worse physical properties, and increased at lower shear reinforcement ratios. However, application methods (SB, UW) did not show significant differences.