In lieu of a vegie dish I make a cucumber salad. The cool fresh taste of cucumber is great with the spicy jambalaya.
Peel ,chop and seed 2 or three cucumbers ( about 2 1/2 cups). Add 1/4 cup of plain yogurt and mix lightly. Sprinkle with a pinch of salt and a table spoon of finely chopped chives.
Chill until served.
Greens would be fine, but if you want to get fancy and really cajun, how about maque choux? It's basically corn, onions, bell peppers sauteed in butter with some herbs and spices. Here's a typical recipe. The cream is optional (I prefer without), as are the colors of the bell peppers you use.
If you can't find fresh corn, cook up something else. This won't be the same with canned or frozen.