What's actually happening at your outlet
Your French drain is doing its job in the trench. The water gets collected and moved. It just can't get out the far end fast enough during a downpour.
That far end is the outlet: either a pipe that daylights on a slope, a pop-up emitter in your lawn, or a connection into a larger drain. When it clogs, everything upstream backs up.
The tell is timing. Light rain drains fine, heavy rain backs up. That points at a partial blockage that only becomes a problem under high volume.
Good news: the outlet is the easiest part of the whole system to reach. You don't have to dig up the yard. You work from the end that's already exposed.
Most fixes here cost $30–$200 in parts and take an afternoon. The expensive scenarios (crushed pipe, deep roots, undersized line) are the minority, and this guide helps you rule them in or out fast.
Why French drain outlets clog
Silt is the number one culprit. Fine sediment washes down the pipe over years and settles at the lowest point, which is right at the outlet. Heavy rain carries even more, and eventually the last few feet pack solid.
Pop-up emitters are the second big offender. The spring-loaded lid is supposed to pop open under pressure, but silt, grass clippings, and mower blades jam it shut. When it won't open, water has nowhere to go.
If your outlet just daylights, leaves and mulch pile against the opening and form a dam. During a storm, more debris floats right into the mouth of the pipe and seals it.
Roots find the moisture. They push into slotted pipe and pipe joints near the surface, then catch every bit of silt that comes down. A root mass turns your pipe into a strainer.
Animals move in. Chipmunks and mice drag nesting material into an open outlet, especially in fall. A single nest can block the pipe completely.
Last, and least common: the drain is just too small or too flat for the water you're throwing at it. If it flushes fine with a hose but drowns in a real storm, that's a sizing problem, not a clog.