The Tolkien language influenced by Finnish is Quenya.
Quenya is one of Tolkien’s constructed Elvish languages and is associated especially with the High Elves. Tolkien developed its sound and grammar over many years, drawing inspiration from Finnish as well as from other languages, including Latin and Greek.
Within the legendarium, Quenya is related to the languages of the Eldar and is treated as an ancient, prestigious language. It appears in names, poetry, formal speech, and phrases such as “Namárië,” Galadriel’s farewell song in The Lord of the Rings.
Quenya is often confused with Sindarin, another major Elvish language. Sindarin became the everyday Elvish language of many Elves in Middle-earth, while Quenya had a more formal and historical role in much of the later setting.