As the Java applet has to respect your proxy settings, first try if the Java applet uses simple HTTP requests by setting up a small logging proxy, possibly through HTTP::Recorder or HTTP::Proxy.
If the Java applet connects through a different port than port 80, and doesn't use HTTP, you will have to break out an actual network sniffer and sniff the connection. I would use Net::PCap as the sniffer, because in the end you will want to write Perl code to emulate the Java applet anyway, but of course if you're more comfortable with ethereal or tcpdump, use that.