Even though the papermaking machine was invented in France in 1798 by Louis-Nicolas Robert, its early development occurred in England beginning with John Gamble's patent of 1801. As a result, the papermaking machine came later to France. That papermaking machines and rotary printing presses were developed in England before their development in France and Germany was the result of the late arrival of Industrial Revolution that began in England in the mid-18th century, but did not get fully underway in France or Germany until the 19th century—as late as the 1830s, by some calculations.
By 1811 at least two inventors in France after Robert were attempting to mechanize the papermaking process. One was Ferdinand Leistenschneider of Dijon, who obtained some brevets or patents for his inventions. At Dijon in 1815 Leschevin and Antoine published a small pamphlet of 32 pages on Leistenscheider's attempts at making papermaking machines. Their pamphlet, Rapports lus a l'Académie des sciences, arts et belles-lettres, de Dijon, dans ses séances particulières des 3 juillet 1811 et 19 mai 1813, sur les machines à fabriquer le papier, inventées par le sieur Ferinand Leistenschneider, fabricant de formes à papier..., appears to have been printed on hand-made rather than machine-made paper, probably because Leistenscheider's machine was not truly operational. It is probable that this pamphlet is the first separately issued publication on papermaking by machine in France, and one of the very earliest published anywhere.
The first papermaking machine was set up in France in 1811, by the Berte and Grevenich establishment at Sorel (Eure-et-Loir). The Berte machine was constructed by M. Calla, "an ingenious French mechanic", but Berte's machine was considerably inferior to the English Donkin machines, and it was Donkin machines that eventually established the French machine papermaking industry, beginning with the first importation of a Donkin machine into France in 1822.
"In 1827 there were four paper-machines in France. In 1833 the number exceeded twelve, according to Proteaux. For the most part these machines were built in England" (Hunter, Papermaking: the History and Technique of an Ancient Craft  536).
Antoine-François Berte, who developed the first operational papermaking machine in France, obtained Brevet No. 1455 for the machine on 11 Octobre 1811. Berte's patent was far more detailed and more advanced than the original Robert patent. In 2017 I was able to acquire a volume once in the library of the Val Cognatrix (Saint-Germain-lès Corbeil) chateaux of the papermaker Paul Darblay, who in 1860 bought the Essonnes paper mills, originally owned by Saint-Léger Didot. It was at this location that Louis-Nicolas Robert invented the first papermaking machine. This volume contains four very scarce pamphlets recording in great detail all the nuances of the patent dispute between Didot and Berte over rights to the papermaking machine in France. These pamphlets were all issued for private circulation:
1. Précis et consultation pour le Sieur Léger Didot, contre le Sieur Berte. 26pp. [Paris, 1823].
2. Mémoire en réponse et consultation pour le Sieur A. F. Berte; contre le Sieur Leger Didot. 62pp. [Paris, 1823].
3. Réponse au factum calomnieux publié par M. Berte contre M.Didot-Saint-Léger, sour le titre: Sur quelques modèles faits à Londres en 1816, présentés en 1823 à l'exposition des produits de lindustrie française, et sur le colportage en Angleterre de la machine à fabriquer le papier continu, inventée en France. 35pp. [Paris, 1823].
4. Supplément a la réponse de M. Didot-Saint-Léger au mémoire de M. Berte. A Son Excellence le Secrétaire d'état, Ministre de l'intérieur. 4pp. (This is printed in small folio format on different paper, and folded into the quarto volume containing the other pamphlets.)
Though these documents provide some documentation regarding the earliest history of machine papermaking in France, the titles of the first publications in France printed on machine-made paper appear to be unknown, except that André (p. 89) mentions that from August 1816 Berte began supplying machine-made paper for the production of the Journal des débats.
André, Machines à papier: Innovation et transformations de l'industrie papetière en France 1798-1860 (1996).