Today I excavated the old french drain that had been laid and is connected to my downspout and my neighbors. I discovered that while they use slotted drain pipes and some gravel on the bottom, they did not wrap the pipe or the trench or cover the pipe in gravel. Everything I pulled out was clogged with silt and near the last T, there was a crushed pipe that most likely is the reason my neighbors yard floods into mine during every rain.

It looks like I will be able to re-use the existing pipe. I will have to replace a portion of the crushed pipe to prevent the water from backing up in that pipe.