This paper is a study of nuclear reactions involving 12C + 12C nuclei carried out with a heavy-ion nucleus-nucleus optical potential derived from a new M3Y-type effective interaction, called B3Y-Fetal, within the framework of optical model at the incident energies of 112, 126.7, 240, 300, 1016 MeV. Folding analyses of the differential cross sections associated with the elastic scattering of the nuclear system, determined at these incident energies with four B3Y-Fetal-based folded potentials constructed from double folding model, have shown the DDB3Y1- and BDB3Y1-Fetal potentials to be the best in excellent agreement with previous work done with the M3Y-Reid. The agreement of the B3Y-Fetal with the famous M3Y-Reid effective interaction, which is also used for folding analysis in this work, is further buttressed and well-established by the findings of this study Herein, the values of the renormalization factor, NR ranging from 1.1117 to 0.8121, obtained with the B3Y-Fetal have been found to be slightly higher, with lower reaction cross sections, aR = 1418 - 1047 millibarns, than NR = 0.9971 - 0.8108 obtained with the M3Y-Reid effective interaction whose accompanying reaction cross sections, being higher, range from 1431 to 1050 millibarns. This depicts the B3Y-Fetal as having a better performance. Additionally, results of folding analyses have shown the best-fit folded potentials, DDB3Y1- and BDB3Y1-Fetal potentials to be in agreement at all incident energies, implying that the cold nuclear matter has an underlying soft equation of state.