The present study focuses on the production of pomegranate alcoholic beverage (PAB) from juice of the Wonderful variety. The effect of fermentation temperature (15 and 25 °C) and type of sugar added (adjustment to 20 °Brix) on the physicochemical characteristics, bioactive compounds, and volatile composition were studied. Sucrose, concentrated pomegranate juice, concentrated grape juice, and honey were used to increase the initial sugar content. The produced PABs contained ethanol in concentrations ranging from 7.9 to 10.0% v/v and glycerol from 4.8 to 6.1 g L−1. A decrease in total phenolics content, free radical-scavenging activity, and total monomeric anthocyanin content was observed following fermentation. Total flavonoids content appeared to increase after fermentation only in the cases of concentrated pomegranate and grape juice addition. In general, 22 volatile compounds were identified in PABs (13 esters, 2 fatty acids, and 7 alcohols). Major compounds detected were 3-methyl-1-butanol, 2-methyl-1-butanol, 2-phenylethanol, and ethyl acetate. These findings demonstrate the production prospect of PABs with increased ethanol content, while elaborating on the importance of fermentation temperature and the differences between the selected types of added sugars on end-product composition.