The web application testing framework will be useful for what you ask, it allows you to simulate user interaction (POST, GET, login, clicks, etc.) with the website.
The hard part of your question interacts with the Java applet - not many Webapp testing web templates will let you do this; in particular, I don't know the Python framework that offers this functionality, but, in my experience, I found that HTTPUnit works well with applets. Of course, this is in Java, not Python, but worth checking out.
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