The aim of this work is to provide a new composite material for applications in the thermal insulation of buildings. The composite was made with mortar reinforced with natural fibres extracted from the petiole of the Washington robusta (WR) palm tree. The fibres used were first chemically characterised by energy-dispersive X-ray spectroscopy, scanning electron microscopy, X-ray and infrared diffractometry spectroscopies alongside tensile testing to discover their morphological structure. Afterwards, the fibres were incorporated into mortar with mass percentages varying from 0 to 4% to determine experimentally the thermomechanical properties of the manufactured samples. The chemical findings indicated that WR fibres are rich in cellulose, hemicellulose and lignin, and possess a high crystallinity index, which enhances the mechanical properties and durability of the composite. The density obtained for the composite W2RC4% is 1305 kg/m3 and less than 2000 kg/m3; this composite can thus be classified as a lightweight concrete according to the standard NF EN 206 + A2/CN (2022). The thermal conductivity and thermal effusivity dropped by about 60% and 42%, respectively. Moreover, the WR reduces the compressive strength (76%) and the flexural strength (36%) to minimum values, respectively, of 5.9 MPa and 3.8 MPa. These values meet the mechanical requirements of lightweight concretes (> 3.5 MPa).