A good place to start for this is the chronicle of Fulcher of Chartres. Fulcher participated in the First Crusade and continued writing about events in crusader Jerusalem until the 1120s. He observed that most people went home after the crusade, but those who stayed in the east, and their descendents, started acting like easterners:

“For we who were Occidentals have now become Orientals. He who was a Roman or a Frank has in this land been made into a Galilean or a Palestinean. He who was of Rheims or Chartres has now become a citizen of Tyre or Antioch. We have already forgotten the places of our birth; already these are unknown to many of us or not mentioned any more. Some already possess homes or households by inheritance. Some have taken wives not only of their own people but Syrians or Armenians or even Saracens who have obtained the grace of baptism...People use the eloquence and idioms of diverse languages in conversing back and forth. Words of different languages have become common property known to each nationality, and mutual faith unites those who are ignorant of their descent...He who was born a stranger is now as one born here; he who was born an alien has become as a native.” (Fulcher of Chartres, A History of the Expedition to Jerusalem, 1095-1127, trans. Francis Rita Ryan, ed. Harold S. Fink (Columbia University Press, 1969), pg. 271)

Maybe they wore clothing that distinguished them from their ancestors back in Europe, but Fulcher doesn’t say so specifically. Actually in the first few decades of the crusader kingdom, the Franks (as the crusaders called themselves) apparently dressed differently from the native population of Muslims and Eastern Christians. In 1120 the kingdom issued rudimentary laws (or “canons”) at the Council of Nablus. Canon #16 says:

“If a Saracen man or woman should dress themselves in the Frankish manner, let them be captured and put into slavery.”

The Latin text of the canons is in Benjamin. Z. Kedar, “On the Origins of the Earliest Laws of Frankish Jerusalem: The Canons of the Council of Nablus” (Speculum 74, 1999), but they’ve been translated online by Simon Parsons: http://www.cfoproject.org/resources/#Nablus

According to Kedar, "...this canon aimed...at reducing the likelihood of inadvertent Frankish-Muslim intimacy." (“Canons of the Council of Nablus,” pg. 324). Basically this means that crusaders and Muslims were totally boning, and the church figured that making everyone dress differently would stop it.

Several decades later, in Sibylla’s time, the Patriarch of Jerusalem, Heraclius, visited Europe to ask for assistance against Saladin. No one was interested, according to a French chronicler named Ralph Niger, partly because of the way Heraclius was dressed. I don’t think Ralph has been translated into English, but as Christopher Tyerman says:

“Ralph Niger, admittedly a hostile witness, expressed astonishment at the lavish ostentation, the gold, silver, and perfumes of Patriarch Heraclius and his companions when they passed through Paris in 1184; a display, Ralph declared, no western ruler could match." (Christopher Tyerman, England and the Crusades, 1095-1588 (University of Chicago Press, 1988, p. 39)

As in the movie, Saladin conquered Jerusalem in 1187. At the end of Kingdom of Heaven Sibylla and Balian are in France and King Richard comes to recruit them; of course in real life Sibylla never left, since she was still the queen. She died while the Third Crusade was besieging Acre in 1191.

European chroniclers of the Third Crusade don’t say anything about the way Sibylla was dressed, but they usually thought the Franks in the crusader states lived too extravagantly. One of them noted that some European crusaders started copying that style. They:

"indulged in the amatory life, with songs about women and bawdy feasting...they also delighted in dancing-girls. Their luxurious dress was further evidence of the effeminate life they were leading." (The Chronicle of the Third Crusade: The Itinerarium Peregrinorum et Gesta Regis Ricardi, trans. Helen J. Nicholson (Ashgate, 1997), pg. 299)

I can’t find any references to the way Sibylla looked or dressed in any sources, modern or medieval. But there are some clues from other medieval observers. Muslim visitors to the kingdom sometimes noted how Frankish women were free to wander around on their own and didn’t have to cover up. Usama ibn Munqidh has an anecdote about a Frankish knight and his wife having their pubic hair shaved by a Muslim barber in the public baths in Tyre - he’s clearly making fun of their uncivilized hygiene but obviously he sees Frankish women being much different from Muslim women. (Usama ibn Munqidh, The Book of Contemplation: Islam and the Crusades, trans. Paul M. Cobb (Penguin Classics, 2008), pg. 148-150)

The Spanish traveller Ibn Jubayr saw a wedding in Tyre in the 1180s, in Sibylla’s time, and described how the bride was dressed “according to their traditional style”, so he also doesn’t seem to think Frankish women wore eastern-style clothing. (The Travels of Ibn Jubayr, trans. Roland Broadhurst (London, 1952), pg. 320)

Modern historians typically conclude that the Franks adapted to eastern styles, sometimes, but they didn’t fully assimilate:

"In dress, acclimatization went with loose-fitting clothes, cool fabrics in the summer, furs in winter, protection of skin and armour from the sun by veils and surcoats; some Franks adopted the turban." (Christopher Tyerman, God's War: A New History of the Crusades (Penguin Books, 2006), pg. 237)

Many Franks:

"could afford to dress in fabrics such as silk and cotton, which were prohibitively expensive in the West…” but they still “dressed in a western way, for although some of their clothes might be made from eastern fabrics, they were normally cut in contemporary western styles.” (Bernard Hamilton, The Leper King and His Heirs (Cambridge University Press, 2000), pg. 57-58)

Their clothes

“... were basically European and changed with European fashions. Articles of clothing which could not be found in the kingdom, like berets, were imported from Europe. And the Franks' sense of ethnic identity went so far that they prohibited non-Franks from wearing European-style garments." (Joshua Prawer, The World of the Crusaders (Quadrangle Books, 1972) pg. 87)

In addition to the works quoted above, some other possible sources to check out are:

- Bernard Hamilton, “Women in the crusader states: the queens of Jerusalem (1100-1190)” in Medieval Women, ed. Derek Baker (1978)

- Susan Edgington, Sarah Lambert, eds., Gendering the Crusades (Columbia University Press, 2002)

- Natasha R. Hodgson, Women, Crusading and the Holy Land in Historical Narrative (Boydell, 2007)

As far as I can tell, none of these talk about the way Sibylla or any other women dressed. The evidence for clothing in art, archaeology, or descriptions in narrative sources is pretty slim, almost non-existent. The best we can say is that sometimes the crusaders themselves felt that they adopted a different lifestyle, and Europeans who visited the crusader states found the culture there to be hopelessly decadent. But they probably didn’t dress too differently than their European relatives, and Muslim visitors thought they still looked pretty much like Europeans.

Also, of course, we should keep in mind that the costuming choices in Kingdom of Heaven are a way to distinguish various characters, good characters vs. bad characters...Reynald of Chatillon didn't really look like an aging hippie, King Baldwin didn't really wear a mask, etc. (Does the commentary track go into this at all? The writer, William Monahan, is on it, but it's been awhile since I listened to it.)