Oddly enough, the larger the vessel the more efficient it is. Sails would be most effective on smaller vessels. A consequence of this is that would become more efficient to use many, smaller vessels with sails instead of "a few" large ships that don't have them.
Or we could just have nuclear powered vessels that emit zero carbon but that'll never happen. Ever since Japan had the genius idea of putting a nuclear reactor on a fault line in a tsunami zone the world seems to be anti-nuclear. Meanwhile, I believe it's the guys who looked at the proposal and said, "oh, yeah, looks good, bud!" should be blamed.
Although, one reason "bunker fuel" is used in this massive ships is that it's essentially a waste product of petroleum distillation and we have nothing to use it for aside from pave our roads in the form of asphalt or just burn it so we can ship products across the planet. Just think of how cheap that means bunker fuel is, it's cheaper to manufacture things on other continents with slave labor and ship it here using bunker fuel than it is to actually pay someone a decent wage to make it.