A simplex-centroid experimental design was used for the optimization of both reducing and oxidizing improvers, namely Aspergillus oryzae S2 α-amylase (Amy), ascorbic acid (Asc), and glucose oxidase (GOD). This optimization was performed to enhance the dough and breadmaking qualities of soft French wheat flour and a composite counterpart that contained 30% Ukrainian wheat flour. Statistically significant correlations were calculated between the W index and textural parameters (e.g., dough chewiness and bread cohesiveness). The findings revealed that while the best mixture for French flour comprised 21.8% of Amy, 41.2% of Asc, and 37% of GOD, for the composite counterpart, it comprised 2.3% of Amy, 66% of Asc, and 31.7% of GOD. These optimized mixtures rearranged soft French wheat flour and its composite counterpart to a good quality and an improved flour texture, respectively. Additionally, they increased the loaf specific volumes of the breads made from soft French wheat flour and its counterpart by 25.8 and 45.43%, respectively, significantly decreased the breads’ susceptibility to microbial contamination, and reclassified the breads as “good” in terms of sensory attributes.