Je veux juste une dernière danse.

signifie je ne veux qu’une dernière danse et non je ne fais que vouloir une dernière danse, ce dernier sens ne me semble simplement pas exprimable avec juste, du moins avec un temps non composé. Au passé composé,

J’ai juste voulu une dernière danse.

et

J’ai voulu juste une dernière danse.

sont tous deux possibles avec la même nuance (mais *je juste veux une dernière danse arrache mes oreilles). Et si on nie, on a aussi des nuances suivant le placement,

Je ne veux pas juste une dernière danse. (J’en veux plus.)

et

Je ne veux juste pas une dernière danse. (Je veux autre chose qu’une danse ; à noter que j’utiliserais plus volontiers simplement que juste ici)

Well, this is a pretty tough question but i’ll give it a shot !
First, here’s how I would put your two choices into other words:

I just want one last dance.

“My only intention is to have one last dance.”

I want just one last dance.

“I want only one last dance.”

For me both answers are correct.
But the first one sounds more likely like a gentleman’s words while the second one sounds more like someone’s who can’t wait to go away.

My advice in those kind of situations is to put your choices in other words and choose which one is more the appropriate considering the context.

Hope that’ll help,
Nicolas.

Actually, “Je veux juste une dernière danse” can be translated by “I just want one last dance”. The word “want” is emphasized, like “hey, I’m not asking much”, meaning that I don’t want anything except one last dance.

“I want just one last dance” would be something like “Je ne veux qu’une dernière danse”, and this means that I do want something, and that thing is only a last dance. The fact that a last dance is not much to ask is emphasized.

For “Je veux juste…”, the most accurate translation is “I just want…”. In French, when we want to express “I want just …”, we will say “Je ne veux rien d’autre que…”

Generally speaking :

- "juste" as an adverb can be translated by "only", "just", "anything but"...

- "juste" as an adjective can be translated by "right", "fair", "just"...

It might depend on where the sentence is stressed.

Je veux juste une dernière danse

could be understood as I just want one last dance.

On the other hand,

Je veux juste une dernière danse

maybe with your index finger pointing up, would rather mean I want just one last dance.

But that will always be a matter of context, of how it’s said, and of how it’s understood.

Juste could be

• An adverb meaning only:

  C’est juste pour rire

  It’s only a joke

• An expression or adjective, meaning right

  Juste, tu as raison! C’est tout juste!

  Right, you’r correct! It’s all right!

• A first name:

  – Il s’appèle Juste Leblanc!

  – Ah bon, Il n’a pas de prénom?

  He’s named Juste Leblanc (not Only Leblanc 😉

  (Le Dîner de cons Zorich662:55)

About little meaning difference between

I’m not completely sure to understand the subtle difference

I just want one last dance.

Je veux juste une dernière danse

and

I want just one last dance.

Je veux une toute dernière danse

« Je veux juste une dernière danse » doesn’t emphasize either one dance or a minor wish. You could translate it as “I only want one last dance” or “my only wish is one last dance”.

The adverb juste doesn’t imply precision, unlike its English counterpart. “Just one last dance” can imply exactly one dance (although someone asking for “just one last dance” is unlikely to complain if granted two), but in French you would need to use some other phrasing such as “une seule dance”. “Je veux une seule danse” implies that you would be unhappy to have two.

If you want to emphasize the “no big deal” aspect, you can say “Je ne demande pas beaucoup, juste une dernière danse” or “Tout ce que je demande, c’est une dernière danse”. If you want to emphasize the single danse aspect without implying “no big deal”, you can say “Je demande une dernière danse, une seule.”