What would improve The Infinity Sword:

What would improve The Infinity Sword would to have a description of its enchantment.
For example: Chillrend's description, "Target takes 20 points of frost damage. Chance to paralyze the target for 2 seconds."

Image example: https://i.ytimg.com/vi/k3RH3rst8jE/maxresdefault.jpg

The Infinity Sword Description Example:
Maybe since when wielded, the effects granted are the Volcanic Invigoration and the Thermal Attunement, the description could be something simple like: "Grants the wielder Volcanic Invigoration and Thermal Attunement."

It's a great sword, but that's the only thing that seems to bother me, because all weapons with enchantments have a/o SHOULD have a description of some sort.
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RECOMMENDED:

Seeing the placement for this magnificent greatsword seems poor. For such a glorified weapon with your backstory at https://steamcommunity.com/sharedfiles/filedetails/?id=151058369 SHOULD make it have a complying location, yes? I found it in Labyrinthian, hoping to find it in some sort of sensible location, but in all the places that seemed good, I couldn't find. I reached the "end" where you take the ladder up to escape Labyrinthian and couldn't find it. I backtracked and looked around the descripted area and yes, I did find it, but the placement was poor. A legendary weapon simply placed on the floor behind an obstruction, it just doesn't make sense to me.

Just my suggestion if you were to place this somewhere as far as vanilla Skyrim, see this video:
https://youtu.be/w8Desd4dbKQ

Fast-forward to 18:10 in the video. That beacon/brazier in the center of the room with the graves surrounding it with the three wisps circling around it - I would suggest leaning or embedding The Infinity Sword into it. That's just my suggestion, if you want it to be in Labyrinthian.
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Why I think it should be placed there:

I think it would be good to place it there because it occurs (if you haven't been in Labyrinthian before) after defeating the dragon and his minions, as well as it resembles that of a reward. After you make your way through and killing this and that, you are in that room shown in the video. Getting to it, you have to get through the gate and it would be decent being in a big room, surrounded by graves, wisps, and a wispmother.

Additionally, there is an Etched Tablet on the beacon/brazier that quotes, "Here Lie the Hollowed Dead of Bromjunaar... May Ever Their Souls Be Their Own."

See wiki on Bromjunaar: http://elderscrolls.wikia.com/wiki/Bromjunaar

Given your description on The Infinity Sword, "A sword of great power that finds its way into the hands of a champion, during times of great peril to Tamriel.” some text supports your quote, as in the wiki states, "During the Dragon Wars, the city went through drastic changes as the ancient Nords rebelled against their Dragon overlords. The city was abandoned shortly after the war and the shrines and temples fell into ruins. It was around this time the powerful priest Morokei was believed to be buried deep within the city." The Infinity Sword may resemble the souls to be forever remembered.

Other: http://www.uesp.net/wiki/Skyrim:Bromjunaar_Sanctuary

Also, obtaining it in that location would be cool in defeating Morokei, and the elf at the end. Just receiving it before a big boss like that is neat, that way you really have something to test it on, including the NPCs protecting Morokei up on those high-up pillars considering that The Infinity Sword is a ranged weapon.