The aim of this work was to formulate a gluten-free focaccia flat bread based on rice and corn flour fortified with dry-fractionated pea protein concentrate (55 g/100 g protein content). A simplex-centroid mixture design with ten formulations helped to study how the flour ratios influenced the physical and sensory properties of dough and breads. The special cubic model significantly described all the responses determined in the dough and flour mixes, and most of those determined in the focaccia. The pea protein concentrate influenced the pasting properties of the flour mixes resulting in a decrease of viscosity. The midpoint of the experimental domain (focaccia containing 5 g/100 g of pea protein concentrate and 20 g/100 g of rice flour and corn flour each) was optimal, being not affected by the discolorations typical of pea (a* = 11.97, b* = 31.86, corresponding to an orange hue), having crumb hardness and chewiness of 9.11 N and 4.83 N, respectively, and moderate legume odor and flavor (5.6 and 5.3 c.u. in a 0–9 scale, respectively). The selected formulation could be labelled as “source of protein” (energy value provided by proteins >12%), “source of fiber” (fiber >3 g/100 g), and “low-fat” (fat <3 g/100 g).