Major crisis for Christianity
Normally, a 'pagan', or polytheistic religion will always be at a disadvantage when competing against a monotheistic religion. In our world, polytheistic religions in Japan and India are as widespread as they are because the two countries haven't been exposed to monotheistic religions as much as other places have been. Japan was in a self-imposed isolation until relatively recent times and India has been too divided and decentralised and at the same time too difficult to conquer completely to fall under the influence of foreign cultures and religions. Still, in both countries various monotheistic religions have become very widespread, just not as dominant as in other places.
The reason for this I believe is that pagan religions are not perscriptive in the way that monotheistic religions are. They don't really have a concept of sin or good and evil and generally don't concern themselves with morals and the right and wrong way to live. Pagan religions are really just extensions of a particular culture's creation myths. Pagan gods usually don't care about human affairs all that much and their worship is usually pretty transactional - you build a temple to a pagan god, or sacrifice some cattle (or some people) to it, and it gives you a good harvest this year. In particular, in pagan religions there is no drive to spread their religion.
Rulers of pagan lands were often pretty happy to adopt a monotheistic religion if they saw it as advantageous for them - abandoning beliefs in pagan gods wasn't that big a deal. But a monotheistic religion views abandoning it as heinous and terribly sinful and just a major no-no. So while there are many examples of pagan territories adopting monotheistic religions, I can't think of a single example of a territory abandoning its monotheistic beliefs and going back to a pagan religion. It's completely unheard of.
So it's difficult to see how your Pagan revival could happen. The only way I could see it happening would be some really really major crisis in your not-Christianity. Perhaps there were widespread and really terrible abuses by the clergy. Now in our world the reaction to abuses by Christian clergy was establishment of heresies that eventually led to religious movements such as the Protestantism, but Protestant religions were still very much Christian religions. But perhaps in your world the clergy managed to somehow discredit themselves and antagonise the populace so much that they turned away from the your not-Christianity altogether and started looking towards the old gods for protection.
Or, perhaps your Renaissance brings a complete rejection of religion altogether and a widespread atheism. But many people, rather than taking a completely atheistic stance, instead adopt a half-hearted and mostly cultural belief in old pagan traditions, in the same way that many people today follow various New Age beliefs and practices.