You're right to avoid using Tolkien's language. I doubt Tolkien's estate would be too pleased about that.
The simplest way to write the scene without inserting the language is to use the viewpoint of someone who doesn't know the language. You can then write something like--
Adam listened to the two elves talking to each other. Their language sounded like the wind in dry oak leaves mixed with babbling creek water.
Finally the elf who could speak English said, "Our king says we will not help you."
Or you can have the scene from the viewpoint of the elf who speaks English.
The king said in their own language, "I do not trust these humans. Tell them that I will not help them find passage through our mountains."
Mossbark nodded and said in English to the humans, "Our king will not help you."
This tips works with any language.