Let us know about your equipment.. guitar mainly.. string guage
You might try fretting the E and B string first (pick to check clarity) then fret the G and D string. (strum) If the F and C note stay clear, adjust finger on the A and/or F note. I'm not an instructor so this is all from my experimentation. Also work on the F chord after you have warmed up doing some of your favorite exercises.. Get relaxed..
Good luck and hang in there..
Gordon