I think, that Mme Finet is not of importance ... one finds not much to her.
True, that one cannot find much on her. My point was that the one at the BM, whose author/publisher is unidentified, seems similar to that described in WPC as being by Mme. Finet. There is the relationship to the c.1790 at the BnF, plus there is the misspelling - Nouvel Eteila, and the spelling as 'Eteila' on the cards at the BM.
He had cooperating engravers, and likely also very much persons, who helped in the distribution of his productions. Likely also Madame Finet. We cannot determine, if he himself engraved the deck, but at least he should have had a state as producer or commissioner.
I am not sure about what relationship there is between the Finet and the Grasset Saint-Sauveur, if any. But I think the Finet is a different version to that of the coq-heron et chez Deroy.
The Finet mentions 36 cards (as are those at the BM, 32 picquet and 4 'Eteila', as in Nouvel 'Eteila').
The rue coq-heron, et chez Deroy, does not mention the number of cards, only that there are 42 tableaux, some double, joined with ordinary cards.
The only address I have found re: Finet is the same as that of the 'Robert' (both of which are called: Le Petit Oracle Des Dames. Nouvel Eteila, ou le Petit necromancien; and both being advertised as being available from the same address.)
The 36 card Eteila deck at the BM, which have several elements in common with the 1791 BnF, are all single figure.
The Nouvelle Eteila, ou le petit Nécromancien, Le petit oracle des dames by Finet from the Rothschild collection is described as a:
Divinatory card game with standard piquet pack and four extra cards derived
from the Tarot of Etteilla (Jean-Baptiste Alliette).
Same as that at the BM.
The sheet is divided into 36 rectangles arranged in rows with smaller reserves for the suits on the
right-hand side. The image is etched and hand-coloured, the text is engraved.
The pack here is a standard French piquet pack of 32 cards Ace, King, Queen, Jack, 10, 9, 8, 7, of the usual four French suits but with four extra Ettellia cards.
Again, same as the BM, excepting the BM is uncoloured, and the cataloguer makes no mention of the name Etteilla being misspelt, but have spelt it wrong themselves, but in a different manner. (I found the deck at the BM through searching its database with 'Eteila', it didn't come up searching with 'Etteilla'.)
Depaulis notes that the game draws on another, earlier and somewhat mysterious set of cards, which he called “Jeu politico-divinatoire” (n° 99 in the 1989 “Les cartes de la Révolution” catalogue), which is in the BnF and bears the APR (“Avec Privilège du Roi”) imprint so it must date from around 1790.
Again, same as that at the BM. And clearly different to that of the coq-heron et chez Deroy, with its 42 tableaux, some double-sided.