Porous carbon derived from grape marc (GM) was synthesized via carbonization and chemical activation processes. Extrinsic nitrogen (N)-dopant in GM, activated by KOH, could render its potential use in supercapacitors effective. The effects of chemical activators such as potassium hydroxide (KOH) and zinc chloride (ZnCl2) were studied to compare their activating power toward the development of pore-forming mechanisms in a carbon electrode, making them beneficial for energy storage. GM carbon impregnated with KOH for activation (KAC), along with urea as the N-dopant (KACurea), exhibited better morphology, hierarchical pore structure, and larger surface area (1356 m2 g−1) than the GM carbon activated by ZnCl2 (ZnAC). Moreover, density functional theory (DFT) investigations showed that the presence of N-dopant on a graphite surface enhances the chemisorption of O adsorbates due to the enhanced charge-transfer mechanism. KACurea was tested in three aqueous electrolytes with different ions (LiOH, NaOH, and NaClO4), which delivered higher specific capacitance, with the NaOH electrolyte exhibiting 139 F g−1 at a 2 mA current rate. The NaOH with the alkaline cation Na+ offered the best capacitance among the electrolytes studied. A multilayer perceptron (MLP) model was employed to describe the effects of synthesis conditions and physicochemical and electrochemical parameters to predict the capacitance and power outputs. The proposed MLP showed higher accuracy, with an R2 of 0.98 for capacitance prediction.