Keep in mind that the global birth rate is in a general decline; even amongst Muslim countries, albeit slower than Christian ones (probably due to poverty and lack of access to contraception). And more religious people have more children than less religious people.
So what does this mean? Personally I predict something like this: growing nationalism in Europe leads to demands for decreases in Muslim immigrants, God willing. The areligious population drops and the religious population goes up. This doesn’t mean Catholic families in France will have 8 kids, but they will have kids. The population stabilizes worldwide at a lower rate of growth. I may just be being optimistic, though.
I remember taking a geography class in which the prof discussed population patterns. In the agricultural stage, birth and death rates are high. In the developing stage, birth rates are high and death rates lower. In the post-industrial stage (provided I get the names of the stages right) both the birth and death rates drop, stabilizing the population. Immigrants from lower-stage countries to post-industrial ones begin living at the developing level, the adapt to post-industrial within a few generations.
Remember, it wasn’t too long ago that American nativists were clamoring for laws to keep those baby-happy Irish Catholics out of the country,