The Upanishads entered European thought by an unlikely chain, and the chain matters because it shaped how the West first understood Indian religion.
Dara Shukoh, eldest son of Shah Jahan and heir apparent to the Mughal throne, gathered pandits at Varanasi and produced a Persian translation of some fifty Upanishads in 1657, titled Sirr-i-Akbar, the greatest secret. His premise was that the "hidden book" referred to in the Quran was this, and that Islam and the Vedanta taught one thing. Two years later he lost the war of succession to his brother Aurangzeb and was executed, with apostasy among the charges.
The Persian text survived him. Abraham Hyacinthe Anquetil-Duperron, who had already brought back the Avesta from India, worked from it and published a Latin rendering at Strasbourg in 1801-1802 under the title Oupnek'hat, a translation of a translation, syntactically Persian, studded with untranslated terms, and by modern standards barely usable.
Arthur Schopenhauer read it from 1814 onward and never stopped. He praised it in The World as Will and Representation and again in Parerga and Paralipomena, and left on record the remark that it had been the consolation of his life and would be of his death. Through Schopenhauer the Upanishads reached German idealism and, by other routes, Emerson and the American transcendentalists; Paul Deussen later produced serious German scholarship on them and became, not incidentally, a friend of Vivekananda. The nineteenth-century European habit of treating the Upanishads as the real Hinduism and everything else as decline traces largely to this line of transmission, a judgement Hindu reformers found useful and Hindu practice never reflected.