Over the years, the development of adaptable monitoring systems to be integrated into soldiers’ body gear, making them as comfortable and lightweight as possible (avoiding the use of rigid electronics), has become essential. Electrospun microfibers are a great material for this application due to their excellent properties, especially their flexibility and lightness. Their functionalization with graphene nanoplatelets (GNPs) makes them a fantastic alternative for the development of innovative conductive materials. In this work, electrospun membranes based on polycaprolactone (PCL) were impregnated with different GNPs concentrations in order to create an electrically conductive surface with piezoresistive behavior. All the samples were properly characterized, demonstrating the homogeneous distribution and the GNPs’ adsorption onto the membrane’s surfaces. Additionally, the electrical performance of the developed systems was studied, including the electrical conductivity, piezoresistive behavior, and Gauge Factor (GF). A maximum electrical conductivity value of 0.079 S/m was obtained for the 2%GNPs-PCL sample. The developed piezoresistive sensor showed high sensitivity to external pressures and excellent durability to repetitive pressing. The best value of GF (3.20) was obtained for the membranes with 0.5% of GNPs. Hence, this work presents the development of a flexible piezoresistive sensor, based on electrospun PCL microfibers and GNPs, utilizing simple methods.