French Drain Help !! (photos included)

[Dogowner]

Here is my problem:
2 dogs and a backyard that slopes towards our house. Currently have surface drains tied into gutter drains & exit into street(circled in blue in photos) which don't do anything. Lawn was destroyed last winter because of poor drainage/dogs and I'm starting to plan everything out to try to prevent this from happening again.

I want to install french drain (highlighted in red) and connect it to existing gutter drain which goes to street. Then resod lawn and hope it holds up this winter. My question is this.... Can I have some of you people look at tell me if you think the french drain will work? I mean is there a big enough slope towards the house to make it worth while? Home inspector said that is what we should do when we bought house last year.

Notice the pictures of where the water pools during rain and how muddy it got last winter. Thanks for any opinons !!!
Here is link to pictures, just click on French Drain Folder

[mrcaptainbob]

Now that's just plain weird. I click on that link and it takes me to my own photo album!

[Troy]

Here are some images that should help with a response: