How to install field lines for the Washer

I'm replacing lines in the house that I'm living in. The washer has been backing up to the point it is over flowing and running down the wall. I went outside and started digging and found the drain line. It looks as though the previous owner used a french drain system. Is this what is normally used for the water from the washer? If this is the answer, how do I reinstall this system? or how do I need to take care of this problem?

Situational awareness: I live in the county. There are no sewage system. We use a septic tank and field lines for our sewage. We have a high water table.