Under the metacity window manager, full screen should work with the standard shortcut defined as you describe in your question, but if you have anything other than "None" selected under System -> Preferences -> Appearance -> Visual Effects, you'll get the compiz window manager. I couldn't find a way to make the full screen shortcut work there either.
You could use the wmctrl utility to send a manual request for full screen mode.
wmctrl -r gvim add,fullscreen
And to revert:
wmctrl -r gvim remove,fullscreen
This even works from within Vim, so you could map e.g. F11 to toggle full screen mode like this:
function! ToggleFullscreen()
if g:fullscreen == 1
let g:fullscreen = 0
let mod = "remove"
else
let g:fullscreen = 1
let mod = "add"
endif
call system("wmctrl -ir " . v:windowid . " -b " . mod . ",fullscreen")
endfunction
map <silent> <F11> :call ToggleFullscreen()<CR>
To get the full fullscreen effect, you could also hide gVim's tool and menu bars:
set guioptions-=T guioptions-=m
I generally don't use either, so I wouldn't miss them. If you do want them in non-fullscreen, though, it will be a little more complicated to toggle.
Finally, a default setting you may have tweaked as you speak of a bottom pane is 'laststatus'. Reset it to not show the status line when there's only a single window:
set laststatus&
(Or preferably find where it's set to non-default in your .vimrc and remove it there.)