Wouldn't the Olympian pantheon be the logical replacement given the large Roman expansion being the thing that drove christianity?
Or potentially the Pagan and/or Norse belief system, which by definition would not have been actively subjugated and turned to Christian purposes, such as the Winter Solstice and Vernal Equinox celebrations becoming Christmas and Easter respectively.
I'd think, if enough if the belief could weather the Roman occupation, we'd be seeing an ascendant Celtic pantheon in the rise of the British empire. The Saxons could potentially sway such, but...
It's an interesting hypothetical that encompasses a lot. For instance, the Roman Catholic church was one of the major reasons that reading and writing survived through the Dark Ages. Without Catholic monks transcribing the Bible and various church documents, and frankly without the Bible itself, which formed the basis of the academic canon, does the written word even continue to exist in Medieval Europe? Obviously, it can always be re-introduced from the East, but what consequences come from a potentially writing-less Dark Age?
Then again, does Europe even go through a Dark Age? I mean, I have no reason to suspect that the Dark Ages were directly or even indirectly caused by the Church. The only thing I can think of is the basically mandatory masses, which could have possibly contributed to spreading disease. Some of the church-fostered superstitions may have contributed, although people would have come up with their own share of superstitions without the Church.
What becomes very interesting then is the lack of the Crusades. Without Christianity and later Islam, Jerusalem is either never taken, or, if it is, it is an event that Europeans have no reason to care about. Of course, most Europeans, or at least the nobles, joined less out of religious conviction and more out of a desire for plunder. But of course, we don't have the Templars or the Teutonic Knights or any of the religious military orders, which changes a lot in Europe.
I wonder also what becomes of the Jewish people in Europe. While Jews have been traditionally persecuted across the world, the two largest contributing factors to anti-Semitism were Christians blaming them for the death of Jesus (which is really stupid when you look at the theology) and the fact that during the Middle Ages, Christians were forbidden by religious doctrine to charge interest, and thus could not realistically own banks, a niche that the Jewish people were able to fill. So it's an interesting theoretical question as to whether the Jewish people become more accepted in a non-Christian Europe, or if losing the advantage of niche banking, while helping them socially, stops them from surviving into the modern day.
I wonder if the Normans invade England in a non-Christian Europe. Again, I don't see why they wouldn't, given the fact that William the Conqueror's invasion did not seem to be religiously motivated, but then again, are the Normans even in power in what is modern-day France? Much of what established the power of the Normans was Charlemagne establishing the rule of the Franks, which he likely could not have done without the pre-existing support of the Roman Catholic Church. It makes me wonder if it would actually be the Eastern Germanic tribes like the Vandals or the Visigoths who take control of Europe. Or then again, does Rome even fall if Constantine doesn't lead them down the path toward Christianity? I suspect it still does, but who knows?
Anyway, that's my twenty-two cents on alternate-reality history.