You could install a trellis on your side.

If the fence is on the property line, it becomes just as much yours as the neighbor who built and paid for it. You can therefore plant something on your side that will grow and drape on the fence without permission but your neighbor always has the option of trimming anything that drapes or scrambles over his side. And once you 'use' the fence (or plant something that grows on it), then you also become equally responsible for its upkeep and repair.

But it is always in the best interest of good neighbor relations to ask first or at least advise your neighbor of your intentions.