The effect of heat treatment on the mechanical properties of two high-carbon-containing (1.5 and 3 at%) single-phase face-centered cubic (fcc) Fe40.4Ni11.3Mn34.8Al7.5Cr6 high-entropy alloys is reported in this study. In the cold-rolled (CR) condition, the 1.5 and 3 at% C-containing alloys, referred to as CR1 and CR2, respectively, demonstrated yield strength values of 1,423 and 1,197 MPa, respectively. The corresponding values of elongation to failure was noted to be 4.05 and 4.46%, respectively. Upon heat treatment at 1,050°C, the CR1 and CR2 samples, referred to as HT1 and HT2 in the heat-treated (HT) condition, demonstrated yield strength values of 358 and 327 MPa, respectively. The elongation to failure of HT1 and HT2 was found to be 37.2 and 26.4%, respectively. The change in mechanical properties brought about by heat treatment was understood by studying the phase composition, microstructure, and crystallographic texture of the material in the CR and HT conditions. Despite the high-temperature heat treatment, the Fe40.4Ni11.3Mn34.8Al7.5Cr6 alloy retained a single-phase structure, indicating good phase stability. However, heat treatment caused a change in the grain structure. The CR materials exhibited an elongated grain structure, whereas the HT materials had an equiaxed microstructure. The CR and HT samples were found to exhibit a weak crystallographic texture although heat treatment had caused the {111} poles to orient themselves parallel to the rolling plane, whereas the CR material had a distribution of {200} poles at 45° to the rolling plane.