How do I attach gutters to a french drain, does the perforated pipe need to run entire distance?
You are trying to combine two systems: 1) collection of ground water, and 2) collection of roof drainage. This is a bad idea...don’t do it. 

1) Perforated pipe is used to COLLECT ground water. The concept behind the use of perforated pipe is that water flows in the direction of least resistance. That is to say, ground water near the perf pipe will flow into the pipe and the remaining water will flow to that area. Then, the process continues until all the ground water has been collected by the perf pipe and carried away. 

Introducing water from your roof into the perf pipe will prohibit ground water from entering the perf pipe system. (You’re defeating the purpose of the perf pipe system.)

2) Solid pipe is used to TRANSPORT water. The water you’ve collected from your roofs should be transported to a storm sewer system...probably in the street. 

When you combine the systems, the water from the roofs will not only prohibit ground water from entering the perf pipe, but will introduce roof water into the ground water system due to a hydrostatic “head” pushing water OUT the perf pipe. (Water can flow both ways through those holes in the perf pipe.) 

Recommendation:

I’d use perf pipe where you have ponding water between the houses and then use solid pipe to transport it to the street storm system. I’d also use solid pipe to collect your roof water from your gutters and downspouts and extend that solid pipe to the street storm system. I would NOT combine the solid pipes, because an abundance of roof water can backup into the ground water system and prohibit it from draining. 

Btw, when you install the perf pipe, be sure to put the holes on the bottom...not the top. You want the ground water to enter the pipe as soon as possible. If you put the holes on top, then the ground water has to fill up to the top of the pipe before it can spill into the pipe.