Many are my names in many countries: Mithrandir among the Elves, Tharkûn to the Dwarves; Olórin I was in my youth in the West that is forgotten, in the South Incánus, in the North Gandalf; to the East I go not.
J.R.R. Tolkien, The Lord of the Rings, The Two Towers
There are currently two competing top answers: the first one says that his "youth in the West" is now forgotten, because it was so long ago and in a different place, or "the West", because it is unreachable and mythical to humans.
How should this sentence be parsed?
For people unfamiliar with the Lord of the Rings, the person speaking in the quote is Gandalf. Gandalf is a lesser God (an angel, or Maia) who might have been born "outside" the world. He spent his "youth" (Maiar do not age, but they can grow in experience and wisdom) in "the West". In a sense, his youth happened either before Earth was created, or in its infancy.
The West is the name given to a continent (Aman, The Undying Lands) that was once west of Middle-Earth, on the other side of the sea. This is where the Gods live. By the time the story takes place in the Lord of the Rings, this continent has been removed from the world, so that
those that sailed far came only to the new lands, and found them like to the old lands, and subject to death. And those that sailed furthest set but a girdle about the Earth and returned weary at last to the place of their beginning; and they said:
'All roads are now bent.'
In this sense, both can be considered "forgotten", either from a time, space or knowledge point of view.
Although it might be a mistake from the translator, the French translation applies "forgotten" to "youth", not West:
Mes noms sont nombreux dans de nombreux pays, disait-il. Mithrandir chez les Elfes, Tharkûn pour les Nains ; j'étais Olorin dans ma jeunesse dans l'Ouest, qui est oubliée, Incanus dans le Sud, dans le Nord Gandalf ; dans l'Est, je n'y vais pas.
I know Tolkien was very protective of his texts and would actively verify translations. He also knew French.