Today, economic and environmental interests have become imperative in construction works. Therefore, the use of substitute materials for natural aggregates or cement contributes to the preservation of natural resources and the reduction of carbon dioxide diffusion. The large quantity of dune sand available in the Algerian Sahara and the affordable cost of recycled aggregates and plastic waste encourage their use as a replacement for natural aggregates in the production of cementitious materials. The interaction of dune sand (DS) and recycled sand (RS) with the introduction of a polyethylene terephthalate (PET-F) fibre help to design a normative ecological material. The aim of the study was to explore and optimize the proportions of these materials to create an environmentally-friendly cementitious product. The strategy is based on the progressive substitution of dune sand by another originating from demolition waste at different rates: 0%, 25%, 50%, 75% and 100%, and a gradual rate of PET-F fibres, 20 and 30 mm from 0% to 2% with a step of 0.5%. In this article, we study the effect of the new composites on the physico-mechanical performance of the designed eco-mortars through several tests (spreadability, fresh density, porosity, capillary and immersion absorption, compression strength, and flexural strength). In addition, we utilise Response Surface Methodology (RSM) to predict approximate parameters that influence the properties of new cementitious composites. The results obtained show the significant benefit of the following rates: 50% SD, 50% SR and (0.5%, 30 mm) PET-F fibre. Thus, the RSM model correlates well with the experimental data, which has undoubtedly led to an improvement in the physical–mechanical characteristics of the eco-mortar studied. Otherwise, the proposed model reaches a high pertinence, with a good desirability coefficient of 0.917.