No, there's no way round it. It is a very deliberate feature that has been designed specifically to stop your applet accessing anything on your computer
No, I'm not kidding - You'll find every browser will behave exactly the same.
The common term for this is the java "sandbox", the term coming from the children's playarea where they can do what they like without destroying anything outside.
The reason for this behaviour is because Applets are most often used over the internet. How would you feel if you visited XYZ.com and ran one of their applets, only to find that the pesky thing had read the files on YOUR hard-disk, and sent all your personal details back without your knowledge??
Clearly, that's unacceptable, and if that COULD be possible, then Java would have died a death VERY quickly. So, as I say, a great deal of effort has gone into ensuring that Java Applets have ABSOLUTELY NO ACCESS **WHATSOEVER** to the computer they're running on.
Since doubtless every hacker would have been trying to break this, and that NO reports of such breaking have ever been received, you can be sure the sandbox is very secure indeed.
What an applet CAN do is communicate back to its host (ie. the machine it was loaded from), and access its resources.