I would say “accordage automatique”

You wouldn’t, like you wouldn’t translate Windows 10 in Fenêtre 10: these are a company’s products.

The underlying technique is Pitch correction, which you could translate as correction de hauteur. But even then, Pitch correction is perfectly understandable by any Frenchie who might have an interest in it.

A lot of technical language (in IT, but also in other fields) has been left untranslated when going from English to other languages for experts from all around the world to understand each other.

Directly from the French Wikipedia page:

Auto-Tune est un logiciel correcteur de tonalité […]

The fact that you have a brand name or that a name was coined after something shouldn’t detract you in any way from finding a translation and explanation for this. An operating system is an operating system whatever the brand name is ; sure one can use Kleenex for tissue but it makes for poor French. Saying auto-tune in French gives you no clue whatsoever about the use of this software or what it does ; I would have guessed it was merely ajusting by itself, as this is what auto + to tune would literally mean, yet that doesn’t cut it as this actually auto-tunes to the proper tone or what not. Finally I’m a native speaker and the word pitch is meaningless to me outside of civil aviation (had to check it’s hauteur ; tangage for flight dynamics), just as pitch correction.