I'm assuming that if you can get from C++ to Java then you are all set. I've seen a product of the kind you mention work well. As it happens the one we used was CodeMesh. I'm not specifically endorsing this vendor, or making any statement about their product's relative quality, but I have seen it work in quite a high volume scenario.
I would say generally that if at all possible I would recommend keeping away from direct integration via JNI if you can. Some simple REST service approach, or queue-based architecture will tend to be simpler to develop and diagnose. You can get quite decent perfomance if you use such decoupled technologies carefully.