We consider a topological Floquet insulator realized as a honeycomb array of helical waveguides imprinted in a weakly birefringent medium. The system accounts for four-wave mixing occurring at a series of resonances arising due to Floquet phase matching. Under these resonant conditions, the system sustains stable linearly polarized and metastable elliptically polarized two-component edge solitons. Coupled nonlinear equations describing the evolution of the envelopes of such solitons are derived.