The present study evaluated the effect of breed, Jaca Navarra (JN) vs. Burguete (BU), and finishing diet, conventional concentrate—diet 1 (D1) vs. silage and organic feed—diet 2 (D2), on the fatty acid composition and volatile profile of longissimus thoracis et lumborum muscle from forty-six foals. For this, foals were reared under a semi-extensive system and slaughtered at about 21 months of age. The outcomes showed that breed and finishing regime had a significant (p < 0.05) effect on the lipid and volatile profile of foal meat. In particular, JN foals reported higher polyunsaturated fatty acid contents and better nutritional indices in line with the health guidelines; whereas, BU and D1 groups generated higher amounts of total volatile compounds. However, it was the diet to occupy a central role in this study. Indeed, diet 2, due to its “ingredients” and composition, not only ameliorated the lipid profile of foal meat, but also reduced the generation of volatile compounds associated with lipid oxidation and minimized off-flavors. Thus, this diet could give an added value to the aromatic perception of meat and improve its sensorial acceptability.