There is a space of about 12" between my concrete drive and the house. 4" perforated PVC pipe is run the length of the house in this space and drains into the yard out back (I believe what is called a French drain). The pipe is covered over with about 6" of clear stone. This drain is under the eave of the house with a gutter, so very little rain water enters -- the drain is really there to deal with snow melt in the spring (I'm in Wisconsin).

At the back corner of the house I have a gutter downspout (3" by 4") that drains half the roof, about 400 sq ft. This used to dump onto a brick patio but this caused water to enter the basement and was damaging the patio. Then I diverted it onto the driveway, but this creates a sheet of ice in the winter. 

Now I have connected it into the French drain. With a light rain, everything works fine. But when there's a heavy rain, the system is overwhelmed and I get water seeping through the foundation into the basement.

**If I were to replace a portion of the perforated pipe with solid pipe, would this solve my problem, or introduce new problems? How far should I go in each direction?** 

Note that I am *literally* between a rock and a hard place here -- a 12" space between a concrete drive on one side, and the house (and then patio) on the other side. The only option to run two systems would be to dig up 50' of French drain and run it deeper, then run the gutter drain over top of that... which might not even be advisable?

Here's an attempt to represent the situation:
 - Black square is the house
 - Gray is the patio
 - Blue is the gutter
 - Green is the French drain
 - Red is the section I propose to replace with solid PVC

[![Drainage schematic][1]][1]