Here's the response from my Archaeologist friend:
"I have him listed as dying at Millen and buried in Trench A at Millen and now interred in plot B2048 at Beaufort. Feel free to have him contact me if they have questions."
Another interesting piece to the puzzle is that, Henry is supposed to be buried in grave 8605, but when I went to look up grave 8605, I also found a reference to a man named S(amuel) Davis, 7th TN Cav being buried there.
http://7thtenncavusa.com/Roster-Da-Di.html I think this identification is kind of sketchy, because it says the guy is paroled, but then recaptured, which did happen occasionally, but the word "presumably" says to me that there are some gaps in the lister's research.
Also, S. Pavies, same regiment and death date also comes up when you google grave 8605, Andersonville. That one may have come from John Ransom's list at the back of his book and is probably a mistranscription/misprint
http://genealogytrails.com/main/military/andersonvilleprisondiary7.html
All three names - Davis, Pavies and Paris, look very close when written in cursive, and could easily be misread for each other. It could be that the expedition that installed the grave markers at the National Cemetery at Andersonville (which originally were marked with just a wooded plank with a number on them), compared the badly written name to a list of prisoners from the 7th TN Cav and decided it said "Paris" so that's the name that they put (in spite of what you may read about Dorence Atwater and his exceptional penmanship, he was not the only clerk writing in the original register, and some of the listings in it are pretty hard to read - microfilms of the original Confederate copy can be viewed on Family Search. It is also not unusual for a name on a grave marker at the National Cemetery to be wrong - case in point, I believe that four of the six names on the Raiders' graves are incorrect (John Sarsfield was James Sarsfield; A. Munn is Andrew Muir; W. Rickson is a misread of a sailor named William Ritson, and Ritson was going by the alias Charles Curtis, who was never actually a POW at all - he was in the hospital with malaria when his regiment was captured; the sixth raider, John Sullivan - almost certainly an alias - doesn't appear on any of the grave markers, but is probably laid to rest in the "Rickson" grave.).
I took a look on Fold 3, and there's no pension file, but his CMSR has him down as dying at both Andersonville and Millen. I can copy it and post it here if you haven't already seen it.
So there are no conclusions - it COULD be that he died at Andersonville and someone went to Millen using his name and died there still using it; or it could be that it's another man from the same regiment at Andersonville and his name got misinterpreted as your ancestor's when they went to mark the graves.
There doesn't seem to have been a pension filed for Henry Paris, which would have required testimony as to his place and date of death from a witness, if any could be found. And I can't find a regimental history book for the 7th Tennessee Cavalry. If you can find any Andersonville diaries kept by a member of his company, there MIGHT be a mention of his death in it - a lot of guys would list the deaths of the men they knew as they happened.
I'll keep thinking about it and see if I can come up with anything else. If you'd like to talk to my friend the Millen expert, I can message you her contact info.