In the original movie, "The Voice" Belongs to an Albanian opera singer named Inva Mula Tchako. The title of this aria or peace she is singing is called Il Dolce Suono. They ONLY edited the part where the pitches changes (towards the end, because a human voice can't change pitches that fast). But those high notes you're hearing are definitely reachable for soprano singers like Inva! Maïwenn the actress only lip synced it!
Upon further research though, there are quite a few people who have attempted the song. I've curated a few for your viewing pleasure. Let me know which one you like the best. I still like the original...
This video shows Inva performing in front of a greenscreen for the movie.
Here's the original scene from the movie.
This incredible young talent sings the song for the Armenian TV version of "the Voice" blind editions!
Evgenia Laguna performing the Diva Song from Fifth Element