French derivation, I think. At first I thought "parterre" but that's not it. I'm thinking about a window or opening cut into a tall privet hedge, usually made of yew or laurel.
How about aperture, which sounds like parterre, but is actually just a fancy word for opening, hole, or gap. From Lexico:
aperture: an opening, hole, or gap
While she was trying to find her way out of the maze, she laid eyes on her soulmate for the first time through an aperture in the privet hedge.
There is this, "The Door in the Hedge". The author might have nonced it somewhere in there.