The main difference between polytheism, e.g. the natural religion, and monotheism is that monotheism is a revelaed religion, meaning that the divine guidance is passed to the masses through people called prophets. Moses, Jesus, Mohammed.
God is above. The ancient gods were not above. No one "believed" in them, because you don't "believe" in air or water. It's just there. The ancient gods were just there, not up in heaven only, they were also pretty much down on earth, more often than not doing quite mischievous things.
I am pretty sure no one in the pre-christian world ever asked someone else "do you believe in the Gods?". It would have been a dumb question and a question you didn't need to ask, since the gods were just there, like air and water.
In the ancient world, the gods were not believed in. They were either feared, or loved, depending on their own behaviour, your state of mind at the time and which one you favoured.
Caesar was no different. Since he was very intelligent he probably was less superstitious than the rest; a few episodes tend to demonstrate that: he once took the axe himself to persuade his soldiers to cut a sacred wood into which they were afraid to enter by fear of the evil spirits.
..And the Ides of March prove that he didn't believe in bad dreams or seers either, apparently..
He stated officially that he was of divine origin and I suppose he fancied the idea that maybe it was true. Whether he actually "believed" it is another matter.