French Drain PVC Size
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.