Hatice Bağana was born in Istanbul in 1932. Her great-grandfather, Mehmed Said Bey (1865-1928), was an interpreter at the Ottoman court. Her father, Mehmet Ali Bağana, was one of the first administrators of the Republic of Turkey, instrumental in Turkish land reform. When he was posted to Paris to work at the OECD, she studied archaeology and the history of art. In 1969, she joined the French National Centre for Scientific Research (CNRS). She obtained her doctorate under the guidance of Emmanuel Laroche in 1973 at the University of Paris I. After Laroche's retirement, she became the head of the Hittitology department at the École pratique des hautes études. She retired in 1997 as an honorary researcher of the CNRS, and was elected as a member of the Deutsche Orient-Gesellschaft in Berlin. Between 1997 and 2011, she taught at the École du Louvre.
In 1964, Hatice Bağana married Antoine Gonnet, a French artist. He died in 2009.
In 1979, Hatice Gonnet-Bağana was in the village of Beyköy, searching for traces of Hittite presence. In 1884, a stone inscription (since lost) of Hittite writing had been documented by W. M. Ramsay, while C. H. Emilie Haspels found second millennium BCE sherds in the area. Gonnet-Bağana's team, hoping to see Hittite artefacts reused locally, was unable to find any, but did establish Chalcolithic remains and determined a Phrygian presence in the area, later reused by Romans. Ramsay's inscription was deciphered in 2017 as writing in the Luwian language (on the orders of a local monarch Kupanta-Kurunta), which triggered further interest in Beyköy. Georges Perrot, a French archaeologist, had claimed that the stone was used in the construction of a local mosque, but this was dismissed by Gonnet-Bağana. Her investigations in the area continued the following year, when she discovered and annotated several rock-cut altars.
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