Garden drainage/ possible French drain installation

Hi all. We moved into our house in Sydney in January. On the building inspection report it was noted that on the southern side of the property next to the wall tends to pool with water after rain. As per the continuous rain over the last few months this has exasperated the issue.

This section of the property is flat. There is a decline from the road down to the to this section which runs flat for approximately 10 meters which the property begins to decline again down to the back fence.


I want to keep this section of the property between the fence and the house as dry as possible to protect the foundation. Would the best option be to install a French drain and turn this section into a rock garden? The issue is we don't have any storm water piping to connect to in the backyard. I'm open to all ideas.

Thanks in advance.