The bioactive conjugated linolenic acid (CLNA) can be microbiologically produced by different probiotic strains when in the presence of α-linolenic acid (α-LNA). Food matrices are a good vector, such as has been previously demonstrated with fermented milk enriched with microbial CLNA by DSM 20091 from lipase-hydrolyzed flaxseed oil. The aim of the present work was to further assess the nutritional, biochemical and organoleptic properties of the developed dairy product, as well as its storage stability throughout 28 days at 4 °C, proving its suitability for consumption. Milk lactose hydrolyzed into glucose (0.89 g/100 g) and galactose (0.88 g/100 g), which were further metabolized into lactic (0.42 g/100 g), acetic (0.44 g/100 g) and propionic (0.85 g/100 g) acids. Titratable acidity reached 0.69% and pH 4.93. Compared with the control (no CLNA), fat content was slightly higher (2.0 g/100 g). Acetic acid was the major volatile (83.32%), lacking important dairy flavor contributors, like acetaldehyde. Sensory analysis revealed predominant astringency and bitterness. No microbial concerns arose during storage, but the CLNA content increased, and some saturated fatty acids seemed to oxidize. In conclusion, the CLNA-enriched fermented milk revealed reasonable compositional properties, yet further improvements are needed for optimal consumer acceptance and a prolonged shelf-life.