Fruit wines have become a popular alternative to grape wines for their variability of sensory properties and unique chemical profiles, offering interesting biological activities. Winemaking also utilizes fruits, which are usually sensitive to biological deterioration, thus reducing post-harvest losses. The quality of wines depends on the fermentation conditions, including the wine yeast selection. In this study, we observed the effect of three common Saccharomyces wine yeast strains on the physicochemical characteristics (color, pH, ethanol content), antioxidant potential (total polyphenol content—TPC, DPPH, and ABTS antioxidant assays), and sensory properties and their relations within plum, apple, and hawthorn wines. Generally, we observed quite-wide ranges in physicochemical properties (pH: 2.8–3.8, ethanol content: 9.0–16.2%) and antioxidant potential parameters (TPC: 0.5–2.4 mg/GAE, DPPH: 0.3–1.4 mg/AAE, 0.5–3.0 mg/AAE), which were affected by the fruit, yeast, and sampling term. The yeast strain significantly affected physicochemical properties and the antioxidant potential on a minor scale. The highest impact of yeast was observed within sensory analyses, where the hawthorn and apple wines fermented by yeast strain Fruit Red exhibited a different sensory profile than those fermented by the Buket and Special strains. A positive correlation between antioxidant potential parameters and their relationship with wine color was confirmed. Moreover, the overall acceptability grew with sweet taste intensity, and panelists preferred wines with lower ethanol content. In general, this study proved the significant impact of wine yeast strain selection on certain qualitative parameters of fruit wines.