The availability of Tritium is a problem for the Deuterium-Tritium (D-T) fusion reactors since the element does not exist in nature and has to be bred from Li-6 through neuron capture. The goal of this paper is to explore a possibility of operating a symbiotic system consisting of fleets of fission reactors coupled with fusion reactors. It is proposed in this paper to use salt with high Li-6 content in Fluoride salt-cooled High-temperature Reactor (FHRs) to produce tritium as fuel for D-T fusion reactors. Tritium breeding blankets will therefore no longer be required, potentially making fusion reactors simpler and cheaper to construct and maintain. Two FHR designs, i.e. pebble bed and prismatic block, are studied in this work to investigate the feasibility of the proposed Fission-Fusion hybrid systems. An investigation into neutronics, tritium production, and potential safety issues in the proposed FHR designs are carried out. The tradeoffs between fission reactor performance, such as achievable burnup and fresh fuel enrichment, and tritium production rate are also discussed. Results have shown that such hybrid systems are attractive and potentially feasible. The maximum tritium production rate of the selected design options can reach up to approximately 4 kg per GW thermal power per year.