I'm not a chef, but I've a little book-larnin' w/ food. Your description of chicken, rice and sausage sounds a bit like gumbo. Gumbo (and jambalaya) are creole rather than cajun, in that they were in Louisiana before the acadians were. That's not to say that cajuns don't make/eat a lot of creole food, just that they're not necessarily the originators.
Gumbo is a sort of stew made with a roux as thickener and flavor, often has bell peppers, onions, celery, okra, andouille (sausage) and some sort of meat. Served over rice.