There are lots of potential PODs that could give you an Islamic Europe by 1500. An earlier collapse of Byzantium is one possibility. A Moorish victory at Poitiers in 732 is another one, though more recent historical work suggests that it's importance has been overrated.
Pointers may indeed be overrated. Arguably a more significant factor in the halting of Islamic spread into Europe was the domination of the Mediterranean by Italian City States. Islam's spread into Italy was halted by them - muslims from spain conquered as far north as Corsica, but only held them temporarily as Genoa, Pisa and Amalfi were able to push them out.
Consider the following;
-Italian maritime republics fail to develop/gain naval superiority in the Mediterranean (not sure how this would be achievedl probably a muslim naval power that could simply field more and better ships than they)
-Norman invasion of southern Italy butterflied away (possibly by aforementioned muslim naval power)
-Lengthy periods where muslims dominate commerce, academia, or just humiliate Christian monarchs enough that their vassals start aligning with the muslims during rebellions frequently.
In this scenario I expect that you could end up with islamic ruling classes (and possibly merchantile classes as well) all across the Mediterranean basin. Northern European states probably remain Christian but aren't part of an organized church (unless the papacy moves north, they'll likely all be parts of independent congregations in the style of early christian Norway) and islam doesn't really make headway into Hungary unless dramatic conquest happens.
Islam probably undergoes more schisms than OTL due to greater cultural overlap - possibly resulting in the establishment of a HRE-style european Caliphate based in Italy.
I think you'll need multiple POD's and a pretty early head start to make all of Europe islamic. Simply an earlier collapse of the Byzantines probably won't cut it; Bulgaria and Hungary (whatever incarnation they may be in) will likely offer heavy resistance. In any case, as with the middle east before recent times when radical demographic shifts led to most non-muslims emigrating, there will likely be significant non-muslim populations across Europe, being a majority in many places.