As both Hogwarts and Durmstrang are in castles and Fleur Delacour said Beauxbatons was a palace, it is likely that Beauxbatons is also inside a castle. Beauxbatons competed in the 1994 Triwizard Tournament. The champion for Beauxbatons turned out to be Fleur Delacour. Fleur wasn't pleased with Hogwarts, and spent half her time bragging about how much better Beauxbatons was.
In Harry Potter and the Order of the Phoenix, Olympe Maxime journeyed with Hagrid to get the giants on Dumbledore's side before Voldemort could. It isn't known who took over the headmastership.
"Beauxbatons" is French for "beautiful batons." The "batons" part is presumably a reference to magical wands.
See Also: Hogwarts School of Witchcraft and Wizardry and Durmstrang Institute