In association with a desirable balance of sugars and organic acids, volatile compounds contribute to the important sensory attributes of apricots. This study assessed the biochemical, aromatic, and sensory qualities of ten Moroccan apricot clones at two maturity stages (M1: commercial stage and M2: consumption stage). Sucrose (1.84–7.09 g/100 g of fresh weight (FW)) and citric acid (0.56–2.25 g/100 g FW) were the main sugar and organic acid in fresh apricots, respectively. The principal identified volatile compounds classes were aldehydes, alcohols, and acetates. The major apricot volatile compounds, hexanal (15.43–696.35 μg/kg FW), 2-hexenal (9.04–404.72 μg/kg FW), β-linalool (8.49–880.50 μg/kg FW), and 1-hexanol (3.35–86.00 μg/kg FW), were previously reported to be major contributors to apricot flavor. Multivariate analysis revealed a significant impact of the ripening stage on the perception of sensory quality related to biochemical parameters. At the commercial stage, apricots were more firm and acidic, characterized by herbaceous odor and high citric acid level, while at the consumption stage, fruits were sweeter, having high reducing sugars (glucose and fructose) contents, and characterized by floral, fruity, and apricot flavors. Among suggested cultivars as suitable for consumption as fruits, red clones (“Cg 2” and “Mans 15”) and orange clones (“Marouch 16,” “Ab 5,” “Rtil 4” and “Marouch 4”) showed very interesting sensory attributes, aroma, and sugar-acid balance, expressing a good overall quality of apricot fruits.