We propose hybrid molecular systems containing small carbon atomic chains interconnected by graphene-like flakes, theoretically predicted as true energy minima, as low-dimensional structures that may be useful in electronic devices at the limit of the atomic miniaturization. The effects of an external electric field applied along the direction of the carbon chains indicate that it is possible to control energy gap and spin polarization with sufficiently high strength, within the limit of the structural restoring of the systems. In this sense, by applying electric fields with magnitudes in the 1-5 V/nm range, we obtain semiconductor-to-metallic transitions for all odd-numbered carbon-chain systems proposed here. Furthermore, high-spin-to-low-spin transitions are determined for these systems as a function of the electric-field magnitude. In the case of the even-numbered carbon-chain systems, the overall electric field effect is pushing electron density near the Fermi level, leading to a gapless or metallic regime at 3.0 V/nm. An electric-field control of the spin-polarization of these latter systems is only achieved by doping the extremities of the graphene-like terminations with sulfur atoms. This finding, however, is beneficial for applications of these systems in spin controlled carbon-based devices connected by gold electrodes, even in the presence of a weak spin-orbit coupling.