The goal for grinding coffee is consistency of the grind, everything should be relatively the same size so it extracts evenly. In coffee grinding parlance, "boulders" is used to describe chunks and "fines" is used to describe microfine particles. When you introduce water (in any extraction method), the "fines" give up their flavor quickly, adding bitterness when overextracted, and the boulders hardly give up anything at all, leaving a thin and sour underextracted flavor.
A burr grinder with two mounted bearings (top and bottom) is the best tool for consistent grinding due to the absence of "burr wobble" seen in cheaper burr grinders.
The Resulting Brew
A sediment layer comes from the fines making their way through the metal screen on the press. Ideally, your goal should be zero fines for your French Press brew. A coffee hack you can do to get around this is to shake your freshly ground coarse coffee in a small metal sieve so the fines fall through. Do this over a container to easily weigh the amount of fines your grinder is producing. I have also seen natural static as a useful by-product of grinding that prevents fines from exiting the grinder.