These things can affect grind buyoancy:
Roast level--lighter tends to be more buoyant due to greater retention of gasses during roasting
Roast freshness--fresher roasts retain more gasses due to less time spent off gassing; this effect is compounded by roast level
Grind freshness--fresher grinds retain more gasses due to less time spent off gassing
Grind level--coarser grinds retain more gasses due to less exposed surface area to facilitate off gassing; this effect is compounded by grind freshness
Brew water temperature--grinds retain gas longer at lower brew temperatures because colder water is a less effective solvent than hot water
Brew duration--the shorter the brew, the more gas is retained. Y the grinds; this effect is compounded by brew water temperature
So your problem is essentially impossible to diagnose without some experimentation. But there's a good chance the sour flavor is not related to the sinking grinds. Most likely, your sinking grinds are due to coffee that has lost most of it's natural gasses. Check the roast date on the bag. Anything older than about two weeks is probably well degassed with whole bean, and anything older than about four hours is likely well degassed with ground coffee. If you grind at home, grind right before you brew to minimize this possibility. But don't feel bad about sinking grinds. They won't affect your brew but might coincidentally be caused by factors that do affect your brew.
The sour taste, on the other hand, probably has to do with extraction as suspected, but the problem is on the other side of things. It's likely that your grind is too coarse and you're under extracting. Try dialing down the grind a bit, and keep your brew time to four minutes (which is the generally accepted ideal for French press).