I tried to look up what a "French Mattress Drain" is, but the results came back that it doesn't exist.
I am familiar with French Drains. As a Home Remodel Contractor, I have quite a few clients that have them. In my experience, all of them love it when they are first installed, and then it's just a matter of time until they stop working and they realize that they wasted their money. How long this takes to happen varies on where it's at, how long it is, and who installed it.
In my opinion, French Drains have become the magical fix to drainage that everyone knows about, but never performs over time.
There is only one sure fired, guaranteed to work method at removing water that is used by Commercial Contractors and Government Agencies. And that is a ditch. Only home owners, landscapers and the guys who mow your lawn, use French Drains. I'm sure there is an exception to this, but it's like saying you wont get cancer from smoking cigarettes'. It happens, but it's not worth the risk of failure.
Nobody wants to dig a ditch because it's a lot of work, and it's hard to make not look like a ditch. You have to go really wide to make it not look like a ditch. Or you have to fill it with gravel, or something to make it look better.
Since most people have to live with a wife that wont approve of a ditch, the only other option that might last is a pipe with a drain to catch the water and carry it away. An open drain can still plug up, but a lot of the time, you can clean it out, and if you are careful with what goes into it, you might get lucky and it never plugs up.