You are using 2/3 cup of beans but you did not mention how much water. There are a LOT of sizes of press pots.
"Coarse grind" really tells us nothing as well. The grinder is also a factor... and the big AND is, what coffee are you using exactly? And how old is the coffee?
But basically, if the taste is thin, grind a little finer and then try using more coffee if that doesn't work.
BUT, I will interject this. IMO, the french press is obsolete. Take a look at the Espro Press. They are about to have a larger model available, and I highly suggest to anyone who likes press coffee to get one. Imagine all the body and rich taste of press coffee with none of the sludge, in a double-walled stainless steel vacuum vessel with a filter system so advanced that you can press the plunger and leave the ground in without fear of over extraction, and the coffee stays hot for a long time as well.
And before anyone asks, I do not work for them nor do I make anything from the sales of this device. I have the original size unit and it makes a GREAT cup of coffee (when fed good coffee, of course).