I have a carbon wing paddle that I use a lot and it is starting to get really faded. It only has light scratches (no deep gouges). I'm guessing if I don't do something the UV will continue to break down the carbon and become a problem. What is the best way to restore the paddle?

I'd start with polishing compound. It may just be surface haze which will rub off.

One of the Meguiars products or TurtleWax polishing compound?.

If that doesn't make a difference, move to rubbing compound.

If something more is needed, then wet sanding with fine (800?) paper.
Then reverse the sequence to get the gloss back....

Automotive 2-part clear coat is quite UV resistant (cars live outdoors a lot..) - if you could get an auto paint place to shoot some on the paddle for a few dollars, it would work well. Single-part 'clear coats' in 'rattle cans' probably aren't as tough.

Or you could do what I did with my carbon Werner Cyprus - spray on a light coat of white paint on the blades.
:-)
Now powerboats have a chance of seeing me..... If I decide to sell the paddle (unlikely) I can always strip off the white paint easily.