Qualitative and quantitative profiles of volatiles in alcoholic beverages depend mainly on the quality of raw materials, yeasts used for fermentation, and processing technique. Saccharomyces bayanus is a yeast species which is not commonly used for the production of alcoholic beverages, but it is able to produce volatiles that add desirable aroma. Since there is little information regarding the application of that microorganism for the production of apple brandies and how it affects volatile profile of finished products, we decided to address that issue. The aim of the study was to determine the impact of S. bayanus on the profile of volatile compounds and sensory properties of apple spirits obtained from three apple cultivars (Topaz, Rubin, and Elise) in comparison to spirits obtained from fermentation carried out spontaneously or with Saccharomyces cerevisiae. Obtained brandies were analysed using gas chromatography–flame ionization detector (GC–FID), solid phase microextraction–gas chromatography–mass spectrometry (SPME–GC–MS) and sensorially. In our study, brandies produced from musts fermented by S. bayanus demonstrated the highest concentration of ethyl esters and increased concentrations of isoamyl acetate, 2-phenylethyl acetate, ethyl palmitate and hexanol. Moreover, our results support the hypothesis that non-Saccharomyces yeasts which are present during spontaneous fermentation and demonstrate higher β-glucosidase activities enhance aroma of alcoholic beverages through releasing aroma compounds from glycosidic forms, e.g., α-phellandrene, (E)-β-fanesene, (Z,E)-α-farnesene, α-farnesene, and farnesol. Considering results obtained in sensory analysis, we proved that S. bayanus is suitable for the production of apple brandies, improving their flavour. Brandies obtained from musts fermented by S. bayanus obtained the highest average range for “overall note” parameter in sensory analysis.