you know, I would not lay any flooring on top of parquet, the reasoning is that the parq I have seen does and can heave and buckle when wet and tends to move and react to humidity and weather conditions, which would make it an unstable sub flooring for any flooring to be on top of. So, I would NOT consider this, I would remove the parq and re lay the laminate, but then I would never use laminate, but that is another topic.
Second, parq, the old stuff is thick enough to sand and enrich and enhance and become a thing of beauty. I would first consider this. Since the parq has wood going in all directions, you need to excercise care in sanding and not use any course paper as I would think this would chip and tear the parq. I would go straight to medium and work down to 220 grit. Then stain it or add oils to it, let it dry then seal it. will look nice.