It's actually rather difficult to find this stuff about the 18th century, particularly accounting that he is likely to have grown up in the South rather than in Paris (since he ended up working in the south). So much is Paris-centric, and/or male-centric. I have sources for the 19th century where I could dig, but a quick run through Google Books trying to find something on the 18th century is not giving me anything helpful. Erica-Marie Benabou might have something in her work on prostitution, but it isn't available online. Patricia O'Brien might have something, but she focuses on the 19th century and her book isn't available, either. Rachel Fuchs on 19th century foundlings won't be of any help.
Not finding anything in French, either, on a quick search.
And this is why you haven't run across anything. There's no great source to run across. If anyone in the fandom has been working on this, they've probably been making things up or not using sources for the right country or right time period. It's very common to not cover this subject - I can tell you quite a lot about the Spinhuis in Amsterdam in the 17th century, and about childbirth in the same period, but not how the two might fit together.
What kind of literature and what kind of life is the same question. - Tom Stoppard