That’s not a huge amount of water. I think the high flow rates paton is on about aren’t an issue for you.
We’ve got springs in our garden and put in land drains a couple of years ago. Trenches lined with Geotextile membrane, gravel, perforated piping near the bottom. I think technically, French drains don’t have the pipe, they’re just filled with rubble, gravel.
Plastic piping is cheaper than the gravel that would fill the space, and it’s lighter to lug about, so it’s a good idea anyway.
Most of ours is perforated all the way round, but for the main run from the main spring, we put in sewer pipe with slots cut in the top. The drain will still take water in from the top, but most of the water being carried just needs to get from one end to the other, and the solid bottom does that without it leeching out in other areas. That’s taking 3,500l a day. Not huge amounts, but more than you’ve got.
Big question is where would you drain the water to? What’s downhill from there?