New advances in materials science and medicine have enabled the development of new and increasingly sophisticated biomaterials. One of the most widely used biopolymers is polycaprolactone (PCL) because it has properties suitable for biomedical applications, tissue engineering scaffolds, or drug delivery systems. However, PCL scaffolds do not have adequate bioactivity, and therefore, alternatives have been studied, such as mixing PCL with bioactive polymers such as gelatin, to promote cell growth. Thus, this work will deal with the fabrication of nanofiber membranes by means of the electrospinning technique using PCL-based solutions (12 wt.% and 20 wt.%) and PCL with gelatin (12 wt.% and 8 wt.%, respectively). Formic acid and acetic acid, as well as mixtures of both in different proportions, have been used to prepare the preliminary solutions, thus supporting the electrospinning process by controlling the viscosity of the solutions and, therefore, the size and uniformity of the fibers. The physical properties of the solutions and the morphological, mechanical, and thermal properties of the membranes were evaluated. Results demonstrate that it is possible to achieve the determined properties of the samples with an appropriate selection of polymer concentrations as well as solvents.