Well, I can think of a couple of possible alternatives, though perhaps very unlikely.
1. There is a Persian equivalent to St. Paul. Somehow this Paulist equivalent plants the seeds amongst the Zoastrian and Jewish communities of Persia that results in the Persians ultimately converting en masse to Christianity in the 4th or early 5th century. With a Christian Persia, perhaps, the Eastern Empire and Persia don't exhaust their military force. The Islamic Arabs, unable to make much headway against the the heartland of the two great Christian empires, instead, fly across North Africa and smash into Spain even earlier than they do in OTL. The Muslims march into Gaul 50 years before Charles Martel and go on to conquer most of Western Europe save perhaps the British Isles and the Scandinavia. Christianity goes on to establish itself in Russia as in OTL, and it gains increasing influence in Central Asia and the Sub-Continent.
2. The Moors win at Tours. The Frankish Empire and much of Western Europe fall to Muslim conquest. While Byzantium can't turn to the West for aid as it did in the 11th century (i.e. the Crusades), it cant be weakened by the later Crusades. Further, perhaps as the one strong remaining Christian State, it becomes a rallying point that allows it to stabilize its borders. Eastern Europe is converted as in OTL but there is renewed zeal to spread Christianity Eastward in Russia. Ultimately Christianity outflanks the Muslims in the East. Ok, this latter scenario is pretty unlikely, but hey, its a thought.
Basically, it is hard to come up with plausible scenarios where Western Europe falls to Islam without the Byzantine empire also falling (being it would essentially under pressure from both sides.).
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Bill