Because what you are describing doesn’t sound like a French drain. I was an excavating contractor for several years and I did install some French drains. The ones that I installed were to deal with high sub water. 5’ deep trench or to bottom of the footing (depends on high you are comfortable letting the water rise up) 3’ wide. Geotextile fabric on the bottom, 4” perforated pipe, 1”-2” washed rock piled a 3 to 4.5’ feet high, geotextile on top again or just wrap the whole trench in geotextile before dumping in the washed rock. Make sure the pipe is sloped the way you want and obviously you have to egress the water somehow. If the ground slopes enough then you won’t need a catch basin and a basin.

Are you just trying to control surface water? If so then you’re approach could work but the best way to deal with surface water is just sloping the ground the way you it even if you need to redo your backyard to get it right. Use a laser transit to get the slopes right.

Let me know if you want any more of my thoughts.