You can't work with files when working with applets. You must use URLs instead. Applet (and therefore also JApplet) has a method called getDocumentBase(). This returns a URL to the HTML file in which the applet is embedded. You can then create a relative URL to the XML file:
Parsing doesn't change much:
Another option is to put the XML file in your JAR file and treat it as a resource. Check out Class.getResourceAsStream for more information.
Edit: beaten by Lester
Oh, and I'll move this to our Applet forum since it has nothing to do with Swing.