The thorium fuel cycle fissile and fusile breeding in a molten salt and a solid fuel blanket for a system consisting of fusion fuel factories coupled to fission satellites burners, is considered. The use of the thorium cycle in a fusion fission hybrid could bypass the stage of fourth generation fission breeder reactors in that the energy multiplication in the fission island allows the satisfaction of energy breakeven and the Lawson condition in magnetic and inertial fusion reactor experiments, hence an early introduction of fusion energy. The nuclear performance of a fusion-fission hybrid reactor having a molten salt composed of Na-Th-F-Be as the blanket fertile material and operating with a catalyzed or a semi-catalyzed Deuterium-Deuterium (DD) plasma is compared to a system with a Li-Th-F-Be salt operating with a Deuterium-Tritium (DT) plasma. In a fusion reactor with a 42-cm thick salt blanket followed by a 40-cm thick graphite reflector, the catalyzed DD system exhibits a fissile nuclide production rate of 0.88 Th(n, γ) reactions per fusion source neutron. The DT system, in addition to breeding tritium from lithium for the DT reaction yields 0.74 Th(n, γ) breeding reactions per fusion source neutron. Even though both approaches provide substantial energy amplification through the fusion-fission coupling process, the DT system possesses marginal tritium breeding in the fusion island of 0.467 triton / source neutron and would need supplemental breeding in the fission satellites to reach a value of unity. Neutron multiplication and flux trap strategies are needed to maximize the fusile breeding aspects. In a solid enrichment factory approach using a flux trap concept and lead as a neutron multiplier to maximize breeding, a tritium yield per source neutron above unity of 1.08 and a Th (n, γ) reaction yield of 0.43 can be obtained for the DT fusion plasma in a concept where ThO2 Zircaloyclad fuel assemblies for Light Water Reactors (LWRs) are enriched in the U233 isotope. This corresponds to 0.77kg/[MW(th).year] of fissile fuel production, and 1.94 years of irradiation in the fusion reactor to attain an average 3 w/o fissile enrichment in the fuel assemblies.