The fact that there is no coordinated response (EU-wide Day of Mourning) to honor John Paul II is an illustration of how big an over-reach the EU constitution really is. There is almost no sense of shared experience across borders. Here's one occasion where the EU had an opportunity to have an agreed EU day of recognition for the exceptional contribution to the development of the European Union made by John Paul II and it doesn't even seem to have occurred to anyone that there should be an EU-wide Day of Mourning.
Each nation is marking the passing of John Paul II in its own way, which is exactly why I think the EU project is doomed. Until the people of the EU feel as one nation, their national sentiments will always trump those of the EU as a whole. Things are bad enough now in relatively peaceful, prosperous times, but what happens if we hit hard times? Yugoslavia might be a model for what to expect.