The lyrics seems written in French/Latin to me, but I can't quiet pinpoint what language the music in. What language is the music in NieR:Replicant?
According to an interview on the Playstation Blog, NieR Replicant's lyrics are written in a made-up language named "Chaos Language" that was created by Replicant's signer Emi Evans.
Perhaps one of its most unique details was the made-up lyrics Emi created, suitably named “Chaos Language”, invented to sound as if our modern languages had drifted away for thousands of years to finally become indistinguishable to us. “The reason we went for this mysterious made-up language is because we felt that as game music, having lyrics which you can recognize and understand might distract you from the gameplay,” explained Yoko Taro, the game’s director, when I met him in 2017 ahead of the launch of Nier’s sequel, Nier:Automata.
Source: PlayStation Blog - NieR Replicant singer Emi Evans talks music, Chaos Language, and more
The same fictional "Chaos Language" was also used for several songs in NieR: Automata.
I recommend reading the full interview with Emi Evans, as she explains the specific languages that inspired Song of the Ancients, Grandma, The Wretched Automatons, and Kainé.