I have a similar issue. On my curtain rod, there is a sort of plastic washer that slides into the outer rod and makes the transition from the inner to outer rod a little bit smoother. If your curtains have metal rings, that might be enough. On my specific rod, the plastic piece is not that smooth, so you may need to shop around, open boxes, and take a look if the rods come with such a piece, and if you think it would be smooth enough.
See the example on this curtain rod:
Also, in my case, I have the curtains on the rod with the loops attached to the curtain, which seem very prone to getting hung up there.My curtain rods are black, so instead of buying a different set of rods, I will try wrapping the spot in one layer of black electrical tape. Depending on what color of curtain rod you have, this may or may not be an option.