In a typical installation french drains are placed around the outside perimeter of a footing of a house to (try to) keep water out of the basement. Obviously this is much easier to do when building the house than after the fact, but it is done both ways. French drains drain to daylight if you are lucky and are on a slope otherwise the drain to a dry well. NEVER connect downspouts from the roof to your french drains. People have done this - it turns out badly unless your intention was to have an indoor swimming pool in your basement.
What you want is to build a dry well to drain your roof gutters into. A dry well is essentially a large hole in the ground filled with crushed stone, with some sort of plastic mesh on the sides and on top to keep the dirt out. You pipe your drain pipes over to the dry well and the water will leach out into the surrounding soil below the surface and out of sight. They can work - or not - depending on the soil type (sand is best) and how much water they are expected to handle. Also if you have a basement keep them away from the house or the water will find its way in!