I have almost exactly the inverse situation. We are at the end of a cul de sac that is capable of efficiently draining water away and out of the neighborhood. But in roughly the spot where your drainage creek is, there's a large strip mall parking lot (across the street from our backyard). We don't get a lot of rain in annual total, but when it does rain heavily a flash flood comes into our backyard and must cross our side/front yard to drain into the cul de sac.

The previous homeowner put in a DIY french drain, but either he didn't do it right, or it's too flat, or it's too small, or it is clogged. We instead get surface water flow and erosion along the same path where the french drain runs.

(It doesn't help that when our neighbors got sand delivered for an above ground pool bed, the delivery truck dumped the entire pile of sand ON TOP OF the river rock exit basin for our french drain. The sand was later removed/used but I was still upset; unfortunately it was my brother in law who ordered the sand. Since the drain is above it I don't think it went in the drain, but maybe this rock basin was supposed to be a dry well.)

I am thinking of building something like your concrete berm along my back fence line, possibly modifying the french drain to just transfer the water from the far side of the berm to the exit over the cul de sac rather than trying to absorb it from the ground.