Another synonym for elephant path: desire line. According to the Wikipedia:

"A desire line is a path developed by erosion caused by animal or human footfall. The path usually represents the shortest or most easily navigated route between an origin and destination. The width and amount of erosion of the line represents the amount of demand. Desire lines were used in early transportation planning, prior to the advent of computerized models. They are manifested on the surface of the earth in certain cases, e.g., as dirt pathways created by people walking through a field, when the original movement by individuals helps clear a path, thereby encouraging more travel. Explorers may tred a path through foliage or grass, leaving a trail "of least resistance" for followers."

In french people say "chemin de l’âne" which means "donkey trail".

Related: How to kill an elephant path and here.