They won't suck up this much water.

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.

That could be simplified by ditching the tank, running a full length 2" discharge, and popping it above ground and into some form of decorative discharge pushing water into the street.
The neighbor probably would not approve of me blasting water and mud onto his car.

Although, the basis has merit. I just need to find the proper discharge feature.

Since you have a shop and fabrication experience just build a flat metal “slot” discharge across the end of your driveway strong enough for vehicles to drive over.
There will a slight decrease in discharge head seen by your pump if the water velocity at discharge is low and exit point a few inches lower. both of which will result in a slight increase in gallons per minute.

Discharging across the driveway to street apron might be considered safer than the wet sidewalk situation.

Pump
2" discharge underground
double 45 up above ground about 6 inches
8" length straight horizontal pipe and double 45 back underground
garden hose bore under side walk 2" pipe install
sawcut curb
put discharge pipe in
concrete curb back
No need for any check valves or additional equipment
Have a beer and wait for rain

It turns out the city has costly and in-depth requirements for curb cuts. That's not gonna happen.

I think I'm going back to 2" pipe for the full distance. It will be much easier to get that under the sidewalk. I can step up to 3" after the walk and terminate in a 6" diameter catch basin. The basin will be topped by a 6" pop-up discharge. That can be changed out for a grate if necessary.
The basin will be perforated and set in a deep bed of rock. It can be surrounded by pave stones to prevent a muddy mess.

The parkway beside the curb is in the utility right of way so I have to be willing to lose anything placed out there.

Locate it in the driveway cut, steeper grade/self cleaning. I believe it should be located above grade. The rock in the "gabion" would diffuse the flow, much like an aerator in a fish tank.
Having something that can charge a reservoir (6" pipe 50' long would allow the pump to cycle off earlier and being above grade it's not pushing against (surface) water.
The cap at the end of the perf pipe should be accessable to clean out.

Usually, at least locally, there is a law against pumping into sewer line. Here there is a new rule that you can't pump into street, "ice patches".

Typical city government.
They originate a problem by not have a stormwater collection system,
then make it expensive and burdensome for those forced to pump stormwater away to prevent foundation problems.

Since you already announced your will be installing a second pump, reconsider going back to 2 inch.

Bigger pipes are cheaper per gallon moved over a decade.

You or the next owner of the property are going to be pumping for decades.

The multiple thousands of $ you had to spend on the foundation stabilization was a penalty for not pumping earlier.

Ancient fortresses had good stormwater drainage because they did not want their walls to collapse.

Before cannons how did attackers get walls to collapse?

Look up what “Sapper” originally meant.

Where is the sewer line?

I'm not going anywhere near the driveway. Future plans involve widening the drive.

As for the second pump, it will be on the other side of the house. There is enough lump in the yard on that side to run a 3" pipe.

I can't do the gabion wall because that involves building a structure on the right of way. It will be in the way of where my neighbor parks now and where I plan on moving the driveway later.