"I 'ave nevair been more insulted in my life! 'Alf-giant? Moi? I 'ave - I 'ave big bones!" - Madame Maxime (GF23)
Olympe Maxime was the headmistress of Beauxbatons Academy in France. She was respected both for her work at her job (GF29) and for her wizarding power (OP20). Though she was a half-giant with the height to prove it, she publicly denied her giant ancestry (GF23) and ran counter to all stereotypes of giants, as she dressed elegantly in silk and jewels, and was an excellent dancer (GF29). She bred Abraxan horses (OP20).
During her year at Hogwarts for the Triwizard Tournament, Madame Maxime became good friends with Rubeus Hagrid, and may have even shared his romantic interest in her, though whether her interest was genuine or a simple desire to get inside information on the Tournament was open to interpretation. Most likely, the truth fell somewhere in between (GF19, GF23, GF28).
Despite her hesitations to admit her giant heritage, Maxime agreed to go with Hagrid as an envoy to the giants in the summer of 1995. Though it was a rough journey, she managed it well (OP20). Madame Maxime also returned to Hogwarts in 1997 to attend Dumbledore’s funeral, where she and Hagrid greeted each other warmly (HBP30).
Olympe = French word for Mt. Olympus, the home of the Greek Gods and Titans.
Maxime = Latin "maxima" meaning greatest or largest, which is appropriate for a woman who is half-giant.