From My Notebook no 4
Some years ago I bought a copy of a small booklet by I. C. Lundberg, "Turgot’s Unknown Translator: the Reflexions and Adam Smith", 1964, The Hague, Martinus Nijhoff. It is inscribed “to Margaret McLennan, playwright from the author & her friends”. Lundberg was a sociologist exploring the foundations of Capitalism, which led him to “an exhaustive study of the sources for capital theory”.
Lundberg’s is a detailed account of every edition and separate printing of Turgot's “Reflexions sur La Formation and the Distribution des Riches” from the ‘first edition’ published anonymously in serial form in a radical journal, Ephemerides du Citoyen, 1769-1770. Turgot composed it composed in 1766. It appeared in book form in French, again without an author’s name in 1788 and in English in 1793, as “Reflections on the Formation and Distribution of Wealth” (Smith died in 1790; Turgot died in 1788).
Condorcet, who was well known to Smith, as was Turgot, in his book, “The Life of Turgot”, wrote: “this Essay may be considered as the germ of the Treatise on the Wealth Of Nations, written by the celebrate Smith” (1786). Smith commenced writing what became Wealth Of Nations in 1763 after several years of delivering his Edinburgh Lectures in 1748-1751. This chronology complicates without determining the facts of precedence.
Lundberg details in the next 52 pages, why he believes that Adam Smith was the translator from the original French (1766) into English. In his short booklet, Lundberg displays shows considerable detective work though all the editions of Turgot’s Reflexions and various printings to make his case.
He also provides a convincing case why Turgot sought and maintained his anonymity throughout his extensive writing career and why Smith respected and protected his wishes. Turgot held a senior post in the repressive State of Louis XVI as “The Comptroller General of the Finances of France from 1744 to 1776" (he died in 1781).
I cannot summarise the case here and do justice to Lundberg’s impressive scholarship. I can recommend that you read a copy in any good library that you can access.
We know that Smith’s literary French was good enough from his translation of Rousseau’s, Discourse on Inequality, 1755 that he published in 1756 in a letter to the Edinburgh Review (see Adam Smith’s “Essays in Philosophical Subjects”  1975, pp 229-256, edited by Andrew Skinner and Thomas Wilson, Oxford University Press.
[Note: I should add that anecdotes about the opinions of high-status French ladies in Parisian Salons may be unreliable given Smith rural Scottish accent and his lack of contact with spoken French throughout is life. He read and spoke fluent Latin and Greek, and he also read Italian.]