The name is a corruption of Barisan, whose meaning I can't locate. Various sites say the pronunciation of "Barisan" changed to "Balian" over the course of the 12th century.
So there was an historic Balian of Ibelin (actually, a father and son of that name) and the movie loosely details the exploits of the younger. Of course, they took a few liberties:
- the family was probably Italian, not French, before coming to the Holy Land.
- the younger Balian was legitimate and wasn't ever a blacksmith or a resident of France. In fact, 10 years before the start date of the movie, he was already lord of Ibelin in the Holy Land.
- his service to King Baldwin is documented and he played a part in negotiating the surrender of Jerusalem. Not sure at all that he was principally in charge of the defense of the city, tho. When he left Jerusalem he fled to Tripoli, not Europe.
- while Balian knew Sibylla, they never ran off together to France. He actually supported her husband Guy for the contested kingship for some time after the fall of Jerusalem, but then shifted his allegiance elsewhere. Sibylla remained in the Holy Land married to Guy until she died in 1190. No happy endings with Balian, sorry.