Installing a drain and connecting to drain pipe

[SammyD]

 

We have had excess run off from our neighbours property(higher level) and they have had the same excess from their neighbours (higher level).

To resolve this, we have decided to do it ourselves and take care of the excess water. In order to do so, I am thinking to install french drain as highlighted in red and connect it to storm drain.

my question is , is that the accurate approach to tackle this and what all pipes, junctions etc will I be needing to be able to do this?