There's something wrong in your calculations or somewhere else.
there's at least one parameter, that's wrong. But I'll stick to the 80W as it's the easiest and simplest.
And you can use a 120VAC rated fuse, no need for 230VAC. But if you don't have a 120VAC one, a 230VAC will do it too.
80W on the primary side means 0,66A of current, which is a constant current, that will be drawn on the primary side, if the ac-dc converter is 100% efficient.
Because we don't know either you have a linear or a switcher power supply (I'll just assume, it 's switched one), you have ~85% efficiency. Lets assume that.
Which means, your constant current flow will rise from 0.66A to 0.77A of constant current(because of losses in your power supply). And since your fan has large starting current, you have to triple it at least, so about 2.1A - 2.5A fuse would be best for this solution (on the primary, 120VAC side).
In this case, you can use a medium-blow or a slow-blow fuse. I would use slow-blow one.
No need for 2nd fuse, if you have one on the primary side. If your power supply is worth anything, it has also an inner thermal fuse, which will prevent destroying the PSU itself.