In this paper we characterize the macroscopic electromagnetic response of a nested wire metamaterial with a high degree of bulk structural asymmetry. The unit cell of the considered metamaterial contains two sets of metallic wires: one set consisting of an array of straight wires and another formed by a racemic array of helical-shaped wires. We study the scattering of electromagnetic waves in a metamaterial slab and show that the electromagnetic coupling between both arrays of wires can originate Fano resonances with narrow line shape. The origin of the resonances is rooted in the formation of a subradiant mode in the metamaterial wherein the net polarization vector vanishes. We envision that the proposed configuration, with sharp resonances whose quality factor can be greatly enhanced by tuning the structural parameters of the wires, may have promising applications in sensing and switching in a broad frequency range from the microwave regime up to terahertz frequencies.