The French press is forgiving in the way that matters and unforgiving in the way you notice. Immersion brewing more or less stops extracting once the coffee reaches a certain concentration, so it is genuinely difficult to ruin the flavour. What it does do, readily, is put grit in your cup.
The ratio is not the one you looked up
Search for a coffee ratio and you will land on 1:16. That is the filter coffee number. Immersion is slightly less efficient at pulling flavour out of the grounds, so a French press wants 1:14 or 1:15 - a little more coffee for the same water.
Grind finer, not coarser
This is the advice that surprises people. Coarse grinding is supposed to stop grit, but the dust that causes grit is a byproduct of the grinder itself, not of the setting you chose. On cheaper grinders, going coarser can even produce more of it. A finer grind extracts better, and the grit is dealt with separately.
Three ways to a clean cup
Plunge slowly and the coffee bed itself acts as a second filter. Break the crust, wait for everything to settle, then plunge - cleaner, but it costs you ten minutes. Or lay a paper filter over the mesh screen, which is the closest thing to a guaranteed result. Whichever you pick, decant into a jug at the end rather than pouring straight from the press.