Gee, all this is fascinating. It's really too bad that the peoples involved simply couldn't stop slaughtering each other, and continued to do so even with modern weapons (such things as machine guns, tanks, etc), resulting in such severe depopulation of Europe by the 1950s that European cultures were unable to pull out of the demographic tailspin, and their reproduction rates became so low that the death of their cultures became guaranteed.
It really matters little who would have taken over, it just happened to be Muslims from Arabia and North Africa. It's to the point now that Canada and the US are more European, genetically, than Europe. Quebec is far more French than France itself, which is on track to become an Islamic nation populated by Arabs and Africans within 50 years. Australia and NZ are far more English than England, which will likely be a Muslim nation of peoples from former English colonies at around the same time that France stops being in any way French. There are parts of the Northeast US that are more Italian, genetically and culturally, than much of Italy, although Italy was not as badly affected by the wars as France and Germany.
North America will probably be a Spanish speaking neo-Central American culture within the next century or two. That will likely make Albuquerque more Spanish than Spain, which has reproduction rates so low that it too is on the fast track towards Islamization. In 200 years English or a variant thereof will be all but dead outside of Australasia. French will likely be a dead language too, as will German and several other Germanic-Scandinavian languages. The main languages to survive will be Spanish, Arabic, and likely Canton Chinese, after southern China races ahead of the north, where Mandarin comes from. Spanish will be spoken in the Americas, Arabic in Europe and the Middle East, and Cantonese in eastern Asia.