The synergistic combination of discrete polymer fibers and continuous textile yarns as reinforcing materials in fine-grained concrete offers significant advantages in the mechanical response of the composite system, including enhanced tensile strength, ductility, impact safety, crack width control, and improved durability. However, the usual high binder demand due to the lack of coarse aggregates leads to an over-reliance on Portland cement (PC) in these composites, negatively influencing their environmental impact. This study aims to reduce clinker content up to 75% by weight of binder using limestone calcined clay cement (LC³) formulations. Tensile tests combined with digital image correlation (DIC) analysis were performed on strain-hardening cementitious composites (SHCC) containing polyethylene short fibers at a volume fraction of 2%, with and without the addition of continuous carbon fibers in the form of textiles. The findings showed that increasing PC replacement in the SHCC decreased the tensile stress-strain behavior. However, incorporating carbon fiber textiles significantly improved the mechanical response, even for the ultra-low clinker hybrid composites with a PC replacement of 75%.