If Europe gets involved, shouldn't they first of all work with the Iraqi people, to help rebuild their country.
The Iraqi people but which one? Which faction? Secular INL-style or Sunni islamists or tribal leaders, the Kurds, the Sadrist Shia nationalists or Iran-aligned SCIRI, the ones inside, the refugees?
"All of them" is alas not an answer. Before Iraq stabilizes if it ever does, it's going to require a few winners and an awful lot of losers.