The cool thing about worldbuilding is that none of it matters. As a writer, you can justify any stupid thing you want.
Is the idea of two rivers flowing in opposite directions rotating a town built on a giant cog stupid? Yes.
But is it awesome? Double yes.
Instead of finding a place with two rivers flowing in the opposite direction, you should find a river with a C-shape curve for your settlement. Those are naturally occurring anyway.
But it would be way more efficient to put the cog right-side up. You would have more surface area in the direction of the water flow for generating power. And the town wouldn't have to rotate either.
Hmm... But the river doesn't always flow at the same rate, so the power output would unpredictable. However, if you dam up a section of the river, you can let the water flow through at a consistent rate, generating power on demand.
And.... now the cool fantasy concept is a modern hydroelectric dam. How drab!

