There is not a European army. The British are in Afghanistan under a NATO mandate. If you remember, Bush said 'you are either with us or against us' when he was trying to recruit for the Afghan crusade. Only Britain took the bait and joined in the invasion.
Eight years later, and it is going pear shaped, why should France, Germany, Italy, Spain, who had the good sense not to join the invasion in the first place (and advised against it), why should they send their young men to be killed?