No one has menitoned that it is important to remember that for good french coffee, in my opinion, you need to use French Roast coffee for optimum results. This results in a very strong, balanced and flavorful brew. Also, don't boil the water. I have a nice electronic kettle that heats the water to 200 degrees. I also use the hot water tap from the dispenser at work normally used for tea and soup. This works very well. Another hint: I can't agree more that you should grind your own beans--I do so at work with a little hand mill--a conical burr grinder. People thought it was strange at first, but now I have people begging me some because it smells so good. I recommend as do others a conical burr grinder because the others, really, aren't that great. I've had the electric ones with the blades and they are quick and easy, but loud and nonuniform. Generally, the more expensive the hand grinder, the better. Avoid the cheapies--but the Japanese ceramic ones look pretty good and are available for a good price. My favorite is a Zassenhaus "knee" grinder that I got recently because it's easy to adjust the grind and the feed mechanism works great with fresh, oily beans. My previous favorite was a Peugeot, but once I started getting really fresh beans that had oil on them, they would get stuck in the feed and I'd have to keep pushing them down by hand--annoying. Plus the Zassenhaus, by far, has the easiest grind adjustment mechanism--you just turn an adjustment wheel. The others have to be partially disassembled, which is a pain. The best part is the Zassenhaus was also the cheapest! But prices have been climbing of late.
I have made medium roast coffee in my french press, and, well, maybe I'm just not a great fan of medium roast coffee, so I won't say that it can't be done, but to be honest, I almost always use French or Espresso roast beans for any coffee in any coffee maker. The larger grind, as I have observed, simply makes the french press easier to clean. The little grinds really get stuck at the bottom of the glass and it takes three or four rinses to get them all. With the larger grind, I get just as many grounds making it through the screen, but I can clean the press with just one rinse. I also like moka style coffee makers--Ikea made an excellent affordable one, which I think was made by Bialetti comparing it to others I own, but I also like drip, and even gasp percolator coffee--which I do think works better for medium grinds. I had an old stove top Corning percolator, the famous white and blue one that everyone's mom had in the 1960s and 1970s and it made, swear to God, the BEST coffee with the most nuanced, nutty, cinnamon, sweet, caramel, roasted, earthy flavor--of course, it only did it once or twice, no matter how many times I tried to replicate it--but no coffee maker I've ever had before or since, and I've had them all, put out results like that. I stick with my french press because it gets pretty close reliably.