The eight kinds of fatty acid binary and ternary eutectics such as capric–lauric acid (CL), capric–myristic acid (CM), capric–palmitic acid (CP), capric–stearic acid (CS), capric–lauric–palmitic acid (CLP), capric–myristic–palmitic acid (CMP), capric–myristic–stearic acid (CMS), and capric–palmitic–stearic acid (CPS) were selected as solid–liquid PCMs in this paper. The innovative electrospun fatty acid binary eutectic/polystyrene/fatty acid ternary eutectic (i.e., CL/PS/CLP, CM/PS/CLP, CP/PS/CLP, CS/PS/CLP, CL/PS/CMS, CM/PS/CMS, CP/PS/CMS, CS/PS/CMS, CL/PS/CPS, CM/PS/CPS, CP/PS/CPS and CS/PS/CPS) and fatty acid ternary eutectic/polystyrene/fatty acid ternary eutectic (i.e., CLP/PS/CMP, CLP/PS/CMS, CLP/PS/CPS, CMP/PS/CMS, CMP/PS/CPS and CMS/PS/CPS) form-stable phase change composite fibrous membranes (PCCFMs) were fabricated by co-electrospinning. The morphological structure, phase change temperatures, and enthalpies were investigated by scanning electron microscope (SEM) and differential scanning calorimetry (DSC), respectively. The SEM images showed that the PS-based phase change composite fibers were collected to form form-stable PCCFMs with the average fiber diameter of about 335–640 nm. The DSC analysis indicated that the melting peak temperatures of electrospun PS-based form-stable PCCFMs can be adjusted to 15–25 °C with the temperature interval of 1 °C by combining the both of fatty acid binary and ternary eutectics into the PS supporting fibers. These PS-based form-stable PCCFMs can be recommended for potential low-temperature thermal energy storage applications to regulate temperature and satisfy the human thermal comfortability.