No European country bears any responsibility for the start of the Syrian Civil War. It was initially an entirely domestic, and secular, rebellion against an oppressive dictatorship.
European countries have virtually no chance of combatting people-smuggling gangs, who almost always abandon their 'passengers' before they reach European shores. That task falls to the 'sending countries' where the gangs are active: above all Turkey, but also Syria, Iraq, Lebanon, Egypt, Algeria, Morocco etc.