Tarnier invented the axis-traction forceps. See also Ann. Gynéc., 1877, 7, 241-64

Auvert described a new and improved closed incubator inspired by a bird/poultry incubator that Tarnier saw at a Paris zoo, and had adapted for human babies by the bird incubator's inventor, Dr. Martin.  Tarnier used that successfully at the Paris Maternité hospital in 1881, and then, with his intern, Dr. Auvard, built a new model superior at regulating and maintaining the babies's temperature. Use of the incubator caused a 50% reduction in mortality. The portion of this extensive French paper in which Auvard described the incubator was translated into English by Egbert Grandin and published as "The incubator for infants," American Journal of Obstetrics and Diseases of Women and Children, 17 (1884) 421-424.  The translation, which includes detailed drawings of the incubator, is available from the Hathi Trust at this link. The French text of the 1883 paper is available from neonatology.org at this link.

(Thanks to Juan Weiss for this reference and its interpretation.)

Tarnier was the first to adopt Listerism in obstetrics. In the discussion following a paper in Trans. int. med. Congr., London, 1881, 4, 390-391, he showed that he was the first to employ carbolic acid solution in obstetrics.