Will constructing a french drain still work using two inch perforated pvc instead of the recommended four inch perforated pvc?
The drain will work but it will not work very well. The larger pipe provides more surface holes for water to enter. The smaller area inside will not have much area for water flow and will fill up with silt more than 4x faster (pie R squared ). Slight variations in slope will affect the drainage. Don’t go with small pipe. Most of the cost in a good drain is digging, and rock. The pipe is a fraction of the cost and trying to go cheep will cost in the long run.
Yes, it will “work” provided 1) an adequate envelope of drainrock around the pipe, 2) the envelope is protected with filter fabric.
1) If you use an envelope of drainrock without fines around the pipe, water will flow to the pipe. I’d use a minimum of 12” x 12” envelope with the pipe in the middle.
2) Filter fabric should encircle the drainrock to keep dirt and soil from flowing through the rock and plugging the pipe.
Remember, water will flow in the direction of least resistance.