Of course europeans had martial arts.. they didn't conquer most of the world with baguettes and bad weather.
I'm not denying that the europeans had martial arts or anything, but which half of the world are you talking about , exactly ? Europe?Most of the time they were busy conquering each other,i don't know if that counts. Excuse me, but it's like saying that the japanese martial arts helped the japanese conquer...the whole Japan.
Apart from the Reconquista (which is not exactly a conquest ,but more like retaking the lands hist. belonging to them), some temrorary successes during the Crusades and the conquests of the Byzantine Empire (which of course started declining after centuries passed and i'm not sure most people would count Byz. Emp. as a "true european" country).
Other than that, i honestly don't see what you mean. The europeans only started to seriously expand "outside of Europe" when the martial arts of the middle ages were either long forgotten or remained as the last resort weapon.
Sorry for the offtopic.