In a forest pool, there is almost certainly some "muck". This is decaying organic matter - probably leaves and twigs for your pool. You may also have inorganic sediment (soil particles) that has washed into the pool. This is usually called "silt", although that is not always technically correct. The silt would also feel squishy to walk on.
I am still not clear, do you have a lower elevation of land available to drain water from your forest pool? If so, then I believe your project should work, and probably provide some relief.
The muck and silt in your pool probably does provide a poor seal. So yes, a french drain on top of the pond muck layer would convey away surface water. However, if it is truly a ground water pond, then getting below the muck and silt would allow you much more efficient drainage of the surrounding aquifer.
Can you dig down a little ways at the edge of the pond? The muck should be a little thinner there before you encounter your true subsoil. If possible, dig a foot or two below the elevation of the middle of the pond to test your deepest layers. If you only encounter clay, then probably NOT a ground water pond.
Just breaching the side wall deeply enough and letting the pond contents run down the slope could be sufficient to drain some ground water away, especially if you scrape some muck away so more of the sand/gravel layer is exposed.
Sorry for the late response. Yes, I do have a lower elevation to drain the pool. The soil is mostly clay unfortunately, which is why is made for a great pond.
I actually already completed the project. Dug up a trench to bury a 3ft catch basin and routed large pvc pipes downhill to the stormdrain. In the first hour or so, most of the pond disappeared. Now its been a day and theres a smaller pool and a small stream flowing into the catch basin. You can see the attached images.
The clay holds so much water it will probably take a long time before it stops being mush, but its slow to release. There has been no change in the groundwater being pumped by my sump as of yet, it has a timer and has been pumping at the same rate even after the pond mostly went away.
I'm hoping its a similar issue here near the sump, mostly clay and has way to much water collected that it will take a long time for the pond being gone to affect it.
I know you mentioned if we hit clay, its probably not ground water. But I just dont see where else the water can come from?