The dual fluid reactor (DFR) is a novel concept of a very high-temperature (fast) reactor that falls off the classification of generation 4 international forum (GIF). DFR makes best of the two previous designs: molten salt reactor (MSR) and lead-cooled fast reactor (LFR). In this paper, we present a new reactor design Dual Fluid Reactor metallic (DFRm) with the liquid eutectic U-Cr metal fuel composition and the lead coolant of which general idea was patented recently. By performing the first steady state neutronic calculations for such a reactor (the neutron flux density as a function of energy, the burnup, the effective multiplication factor/reactivity), we show that this 250-MWth reactor is critical, and that it can operate almost 20 years without refuelling. We also optimise the geometry (reflector thickness, fuel tubes pin pitch) with respect to the multiplication factor. The optimisation together with some other opportunities for the liquid metal fuel design (eg, the use of electromagnetic pumps to circulate the medium) allows DFRm to be of a small size. This rises economy of the construction as expressed nicely in terms of the energy return on invested (EROI) factor, which is even higher than for the molten salt fuel design (DFRs). Last but not least, we show that DFRm has all the (fuel, coolant, reflector) temperature coefficients negative, which is an important factor of the passive safety.