Environmental awareness has led industries and consumers to replace products derived from oil resources with products derived from natural sources. In the case of the composite materials industry, the replacement of synthetic fibres with natural fibres has increased in recent years. To study the influence that different types of natural fibres and different textile manufacturing techniques have on the mechanical properties of composites, bio-based epoxy matrix composites reinforced with different natural animal fibres were produced, some reinforced with sheep’s wool and others with dog wool, which were later subjected to bending and tensile tests. From the authors’ knowledge, there are few studies of composites produced with animal fibres, and even fewer with dog hair. The textile structures used as reinforcement were created using crochet, knitting, and weaving techniques. Prior to the composites production, the fibres were characterized by X-ray Diffraction (X-RD), and the yarns produced from these fibres were subjected to tensile tests. The results obtained suggest that the number of yarns and the diameter of the needles used during the production of the reinforcement have a significant impact on the mechanical properties of the composites. The green epoxy resin composites reinforced with sheep’s wool exhibit higher values of flexural strength, tensile strength, and Young’s modulus than those reinforced with dog wool, with average increases of 36.97%, 45.16%, and 72.99%, respectively. It was also possible to verify that the composites reinforced with woven fabrics and crocheted fabrics exhibit the highest values of tensile strength, flexural strength, and Young’s modulus. Additionally, the composites reinforced with woven fabrics exhibit the highest values of deformation at first failure/break and toughness.