French drain is built above grade. Have the pump discharge line run level in the ground, neck it down at the end (inc pressure) to lift it above grade into a larger solid pipe (reservoir) that runs down hill toward the gabion wall french drain.
That down hill portion of run (reservoir) can be done in the same style gabion wall or could be whatever size pipe or rectangular tank that can be hidden in your landscape and anchored to ground to avoid buoyancy when empty..
The option to place flagstone "cap' on the french drain wall exists.
I believe this concept may work as no grout is required the wall can move with the clay, the pump can shutoff after it charges the down hill run of pipe or storage tank that flows to the french drain.
I believe you sump will need to be sized to handle any back-flow should the back-flow get obstructed. Unsing a tank/reservoir allows the pump to cycle and allows continuous discharge of pumped water.
I can imagine other configurations of tank to discharge that would work.