While a ride on trencher will do it, they are the only ones that will cut a 6" trench, I believe it will be $300-500 a day, depending on machine.  Not worth it for 80ft.
Every walk behind trencher I have rented was only 4" a trencher.  Personally I have grown to detest those things.  The way they (ride on ones too) throw the dirt right beside the hole makes it impossible to go back over any section without risking it dropping a wheel in the hole and then its a whole lot of fun to get out, I know.
I would rent a small excavator or small backhoe.  Around here those go for under $200 a day (one was $165 and the other was $185 can't remember which was which), and if you're making a french drain like I did (mine was 85ft long) it will make it a LOT easier to set the pipe.  You will want a small amount of gravel under it, and on both sides to keep dirt from getting to it and clogging it up.  get a 12" bucket and you will have it done in no time.
My preference would be the backhoe, as they seem like a more stable platform, if you have the room, otherwise get an excavator, they are a LOT more maneuverable.  i have used both on my place.