The fictional language spoken by the Eldar and inspired in part by Finnish is Quenya.
Quenya is one of Tolkien’s most developed Elvish languages. He associated it especially with the High Elves, including the Ñoldor and Vanyar, and gave it a formal, ancient, and literary character within the mythology.
Tolkien’s interest in Finnish, particularly the Kalevala, influenced the sound and structure of Quenya. He also drew on other languages while constructing his linguistic families. The language’s internal history includes changes and relationships that mirror the way real languages evolve.
Sindarin is another major Elvish language, but it developed along a different historical and linguistic path and became more widely used in Middle-earth during the Third Age. Adûnaic belongs to Númenor, while Khuzdul is the language of the Dwarves.