This study describes the production of a new biobased epoxy thermoset and its use with long hemp fibres to produce high-performance composites that are totally biobased. The synthesis of BioIgenox, an epoxy resin derived from a lignin biorefinery, and its curing process have been optimised to decrease their environmental impact. The main objective of this study is to characterise the rheology and kinetics of the epoxy system with a view to optimising the composite manufacturing process. Thus, the epoxy resin/hardener system was chosen considering the constraints imposed by the implementation of composites reinforced with plant fibres. The viscosity of the chosen mixture shows the compatibility of the formulation with the traditional implementation processes of the composites. In addition, unlike BPA—a precursor of diglycidyl ether of bisphenol A (DGEBA) epoxy resin—BioIgenox and its precursor do not have endocrine disrupting activities. The neat polymer and its unidirectional hemp fibre composite are characterised using three-point bending tests. Results measured for the fully biobased epoxy polymer show a bending modulus, a bending strength, a maximum strain at failure and a Tg of, respectively, 3.1 GPa, 55 MPa, 1.82% and 120 ◦C. These values are slightly weaker than those of the DGEBA-based epoxy material. It was also observed that the incorporation of fibres into the fully biobased epoxy system induces a decrease in the damping peak and a shift towards higher temperatures. These results point out the effective stress transfers between the hemp fibres and the fully biobased epoxy system. The high mechanical properties and softening temperature measured in this work with a fully biobased epoxy system make this type of composite a very promising sustainable material for transport and lightweight engineering applications.