Hi
"using fn down" isn't part of System Events' AppleScript dictionary, and so will always give you a syntax error. (Same with "using function down".) You can script command, option, shift, control and combinations thereof, but not the function key.
On my 2012 MacBook Air with a UK English keyboard, I can increase and decrease screen brightness using the following scripts:
tell application "System Events" to key code 107 -- decreases brightness
tell application "System Events" to key code 113 -- increases brightness
It may not work for everyone, and it may not be what you actually want to do. But if you can tell us why you want to achieve by pressing that key combination, there may be other ways.
There is a very useful page here which goes into a lot of detail about key code scripting - definitely worth reading. (It's where I got the key codes for screen brightness.)
One of the points the guy makes is that trying to script the function keys is unreliable and not always possible.
Cheers,
H