French drains are for moving residual water or water left over after the rain event. Those stone basins here are called privy pits. They are also in my opinion too get rid of residual water for example you have a low spot that the water settles in and you cannot get a pipe out of it too a lower elevation. You install a stone basin too allow the water a place too go while the ground absorbs it.
As has been stated grading is the first choice for water issues but sometimes that is not possible so thats when we install drains of some sort. I only use french drains for minor water issues. Up North I know that they are used more than they are here due too differences in soil conditions.