The geometrical configuration of Au:Ag nanoparticle heterodimers can be optimized to produce prominent Fano resonance (FR) signals, strong enough to be detectable by standard spectroscopic techniques. The highest intensity of the FR in these bimetallic dimers is reached when the size ratio of the nanoparticles (RAu:RAg) is close to 3:1. Moreover, the FR can be induced only by the longitudinal component of the dimer surface plasmon resonance (SPR). Finally, it is found that the sensitivity of the dimer FR signal to the variation in the refractive index of the surrounding medium (nm) is 2 times larger than that of the associated SPR for the region where nm < 1.5, which opens up the possibility of utilizing the FR band for more efficient optical sensing applications.