How thick should a french cleat be?
I don't believe the thickness of the cleat is as critical as the type of wall anchor being used.  The cleat holds the cabinet in place, but it's the anchors which are really bearing the weight.  I would make my decision based on the type of wall material holding the cabinet and use an anchor rated for the expected weight of the cabinet for that particular wall material.  If you have a regular drywall and wooden stud construction, I would probably use the screws used to hang kitchen cabinets as they are designed to carry a pretty heavy load.  You could have a 1.5 inch cleat with an inadequate anchor and the cabinets will pull it right out of the wall.