Mike,
How far and how deep do you need to dig the trench to carry the water away with the drain?
The reason I ask is the main advantage to a french drain is cosmetics. The land still looks nice, or smooth after its in.
They are fairly involved, expensive and time consumeing to put in,and there is a finite timetable on how long it will last.
From your picture, you already have a nice wide trench that is collecting water, why not extend the trench and keep it all open?
Or put in a drain pipe?
You can get a roll of 6 inch black corugated pipe 100 feet long for under $50 from Lowes for an aweful lot cheaper than any other type of drain.
A picture of the back and what's holding the water back would be very helpful.
Good Luck,
Eddie