Actually, NewJ Library for C++ from PureNative Software supports implementing Java applets in C++. It supports two different approaches. Choose the one that best meets your requirements.
(1) If you need to run the applet in a Java PlugIn-enabled Internet browser, such as Internet Explorer or Mozilla, you can use NewJNI to extend the JRE's implementation of java.applet.Applet. You'll probably need to grant your Java PlugIn permission to call native methods from your Java applets.
(2) If you would be able to run the applet in a special-purpose Applet Viewer instead of an Internet browser, you can use NewJ Desktop's 100% native implementation of java::applet::Applet. In this case, you can use all your C++ code as is without the considerations and complexities of JNI.