The offshore wind power via flexible low-frequency transmission (FLFT) system based on the modular multilevel matrix converter (M3C) faces power surplus and stability risks following faults on the power frequency grid side. To address this issue, the effects of the M3C power frequency, low-frequency decoupling control strategy on the transient process under grid side faults are first analyzed in the paper. Secondly, boundary conditions for power frequency, low-frequency side voltage and active power are deduced. Consideration into the control methods of the M3C converter, low voltage ride-through requirements, and fault types, a fault ride-through strategy based on an improved voltage-dropping method is proposed for M3C-wind turbine joint voltage-power sag control to enable wind turbine overspeed load shedding outside the low voltage ride-through range. Finally, a wind turbine via a FLFT model is built in PSCAD/EMTDC to validate the proposed strategy. It is shown that the proposed strategy can ensure the average voltage of the M3C sub-module capacitors within limits and enable safe operation during system faults.