Sustainable freshwater aquaculture has been recently gaining attention owing to the potential of nourishing the world. The study aimed to evaluate the influence of finishing diets on the activity of 21 genes involved in hepatic lipid metabolism and intestinal homeostasis, liver and intestine histology, and the level of eicosapentaenoic (EPA) and docosahexaenoic (DHA) acids in common carp fillets. We compared two experimental diets: control diet mimicking a commercial feed (CTRL) and a test diet (CB) fortified with EPA and DHA retrieved from salmon by-products. An additional control (eCTRL) from extensively cultured carps was investigated. The study revealed that the expression of seven hepatic genes, e.g., lipoprotein lipase and fatty acid synthase, and six intestinal genes e.g., claudin-3c and γ-glutamyl transpeptidase, was influenced specifically by the experimental diets and farming type. Fish from the eCTRL group had the smallest hepatocytes and the largest nuclei compared with CTRL and CB. No pathological signs were found in intestine samples. Additionally, the levels of EPA and DHA in fillets were significantly higher in fish receiving CB compared with CTRL and eCTRL. The use of fortified diets is a promising solution to produce freshwater species with enhanced nutritional value without compromising the safety of fillets.