French artist Orlan was asking for 7.5% of the royalties made by the star's record.
That amounts to $31.7m (£28.3m) of the eight million global sales for her second studio album.
The case claimed that Gaga had stolen concepts from two sculptures including a 1989 piece called Bumpload and Woman with Head from 1996.
It was argued that the work had been copied in both the album artwork, as well as in a scene from the music video of the same name, where severed heads appear on a table.
The case also considered Lady Gaga's reading out of The Manifesto of Mother Monster as a reference to Orlan's Manifeste de l'art charnel (Manifesto of Carnal Art).
According to The Art Newspaper, the court's ruling found that an artistic installation cannot be reduced solely to its physical elements.
The ruling also stated that Orlan must pay Lady Gaga and her record label 10,000 euros (£8,390) each, as dictated by France's legal code for civil proceedings.
Orlan told Artnet news that she intends to appeal against the decision.