For simplicity purposes, I'll start from the beginning.
The next time you get a hard rain, go out with an umbrella and 1) watch the water run off the roof, 2) into the gutter(s), and 3) out to the end of the french drain. Assuming 1) the rain is actually running into your gutters and NOT over, under, or beside them, 2) the gutters are properly sending the water to the downspout(s) and not over, under, or beside them, and 3) you see water coming out the end of the drain, I'd assume the problem is from excess water coming down the hill. If the later 1, 2, or 3 aren't doing their job, then start by correcting them before you do any more work.
You didn't mention how close the hill is to your foundation, and you didn't mention what 'slope' you have between the foundation and the bottom of the hill. Is the slope closest to the foundation running AWAY from the foundation? (This is positive slope.) If you have negative slope, water is being encouraged to run towards the house. Now, when you say surface french drains, I'd like to hear from you a short description of what it looks like and where the water from it ends up. It's quite possible that if you, literally, have a surface 'trench' that isn't constructed with perforated pipe under it. If this is the case, then water being absorbed by the ground is working its way to the foundation underground, thus, putting pressure on the outside of your foundation. (But I do need more info.)
Anyway, I've attached a link for you to look at to see if this is actually the type of french drain you had built. Click this Landscaping URL and go to the BOTTOM of the page. On it, you'll see 2 links for your situation under DRAINAGE. The 2nd one actually shows a picture of a french drain. (It reads using 'landscape fabric' where it should read 'filter fabric'. They're different and I received confirmation from the mfgr there that they will correct the mistake.) I'll be out until Monday but will be here for the day. I'll be standing by. My best to ya and hope this helps.