You do want a coarse grind for french press coffee. The key is letting the coffee steep for long enough to make a strong brew. I have good results with a 5 minute steep time. Be sure to use a timer, and compare different times to find the optimal brew. As a general rule, if you are at altitude, then you need to add time because boiling water is cooler. (Note that I am at 5000ft, so 5 minutes may be too long for you.)
Below is a picture of the coffee chunks in a coarse grind on top of a US 5 cent coin (21.21 mm in diameter).
The picture is from this article.
EDIT: The reason to use a coarse grind for a french press is that finer grinds will get stuck in the filter and/or push their way through. This has three potential problems: 1) it will be harder to press down the filter, possibly leading to spillage or breakage; 2) your coffee will have grinds in it; 3) the coffee may become bitter, as the finer grinds that passed through the filter remain in contact with the coffee for too long.
Assuming you're talking about USA usage, you're correct, a "cup" is usually 6oz. In the USA, the standard size for a "cup" of coffee is 6oz, even though nobody drinks cups of coffee that small (12oz to 20oz is more common). For that matter, the size of a "cup" of tea can be 5oz or 6oz when the number of "cups" a teapot holds is listed; a "6 cup" teapot is only 32oz.
However, be careful how the word is used in American recipes. If a recipe calls for a "cup" of coffee, they are more likely to be calling for an 8oz cup, rather than a 6oz cup.
I can't find a clear reference as to where the unrealistic 6oz measurement for a cup of coffee started. Possibly the result of Mr. Coffee, but we're stuck with it as customary now.
However, even though a 6oz cup of coffee may be customary, specific coffee maker manufacturers may use different measurements on different models, including cups as small as 4.2oz. So don't assume unless you've checked.
Oh, and also note that the 8oz cup is American, rather than Imperial measurement. An Imperial cup is around 10oz, although you're unlikely to encounter this measurement in any recipe published after World War I.
Confused yet?
Best Answer
The answer is that it will depend on your personal preference for the strength of your coffee, the beans themselves, the type of brewing, and so on. Many coffee bean bags have a reference on the side of them.
The standard guideline for most medium roast coffee bean bags is 2 tablespoons per 6 fl. oz. (3/4 cup in your 8oz liquid measuring cup).
The Specialty Coffee Association of America has some interesting info on this, per this link.