Predominantly French. Well, if we're being nitpicky, Frankish. See, the first "official" call to crusade came from Pope Urban II at the Council of Clermont (a city in the middle of modern France) in 1095.

This was a strategic decision: the crusade was pitched as a kind of martial pilgrimage to drive the Muslims out of the Holy Land. And so he went to the region best able to provide manpower, leadership, and--most importantly--financing. In the late 11th century, that was France. So while the idea of crusading spread throughout Europe, France was the epicenter, and Frankish aristocrats and Frankish preachers were typically at the forefront of any expedition. (I mention preachers because they were often the means by which the notion of crusading was disseminated and promoted.)

Jonathan Riley-Smith's The First Crusaders, 1095-1131 is a good starting point. If you're really curious, Christopher Tyerman's voluminous God's War is about as thorough an introduction as you're likely to find.

While the Crusaders may have had a majority of participants which who originated in what we would now call France, they were, however, much more diverse than some of the comments here are giving credit to them for. As has been noted, later crusades became even more diverse (with more invovement by English, German and Scandinavian contingents), even the First Crusade was not overwhelmingly French.

The easiest examples are found in the leaders of the First Crusade. Of the three most prominant leaders - Raymond of Toulouse/St-Giles, Godfrey of Bouillon and Bohemond of Taranto - only Raymond can be argued as being 'French. But Toulouse and Provence weren't seen as 'French' in the 11th century, Raymond as Count certainly did pay any attention to King Philip up in Paris and was, in fact, invoved more with the politics of Catalonia than with that of the Ill-de-France. When he went on Crusade, he and his contingent would have spoken a different lanuguage to the crusader contingents from the North of France.

So then we've got:

• Languedocian contingents, led by Raymond and the papal legate, Adhemar of le Puy,

• Southern Italian contingents led by Bohemund,

• German contingents led by Godfrey - which consisted of "Lotharingians, Saxons, Swabians [and] Bavarians", (and later even included some Flemish pirates to act as naval support!)

• Italian Ships and Navies which supplied and supported the Crusaders after the capture of Antioch (who were, IIRC, primarily from Genoa and Pisa, but I don't have the reference with me at the moment).

• And then, finally, the Northern French contingent, with a mix of commanders, including Hugh, Duke of Vermandois and brother to the King of France, Robert, Duke of Normandy and brother to the King of England (who could be argued to represent a seperate 'nation') and Stephen of Blois.

We have no idea of the relative strengths of these contingents, but certainly it was the non-French leaders who stood out and took charge, even in chronicles written by French historians. It has been assumed that French soldiers made up the majority of Crusaders and I certainly wouldn't argue against it, but it's important not to overlook the diversity the army represented. Riley-Smith's First Crusaders, which some other commentators have mentioned, is good at tracing the origins of many named crusaders and, IIRC, places most of the recruitment in central France (Poitou, Loire Valley, Limousin) but this favours areas which have the local (primarily monastic) records surviving through which we can trace crusaders before they left for the Holy Land. It's still an excellent piece of scholarship, but it's almost total focus on France is misleading in identifying the national make-up of the forces of the First Crusade.

In the early crusades, they were mostly French. Later on, they would have been very diverse.
If I remember correctly, Kingdom of Heaven takes place just a few years before the Third Crusade (which was a joint effort of numerous nations including England, France and the Holy Roman Empire, among others). While most of the early European crusaders would have been French, the Second Crusade received much larger participation from a multitude of places outside of France. In between crusades countless men of other nationalities would have been pouring into the Levant, both as crusading warriors as well as pilgrims. The European-controlled Kingdom of Jerusalem had been well established, and people of all nationalities lived there.
In addition, several of the Levantine holy orders had been formed, including the Templars and Hospitallers, both which play a role in the movie. Those orders received support from basically every nation in Europe, including drawing noblemen into their ranks.
Though not stated outright, it appears that the ragtag group of crusaders in Kingdom of Heaven may in fact be a group of Hospitaller Knights. (David Thewlis's character is simply named "Hospitaller"). If that is in fact true, it would not be at all surprising to find their group composed of various nationalities. Hospitallers were known at times to be especially tolerant of "The Other", given the circumstances and time period. They ran a rather large hospital in Jerusalem, and were known to lack any discrimination in who they treated.
"Knowing that the Lord, who calls all to salvation, does not want anyone to perish, [the Hospital] mercifully admits men of the Pagan faith [Muslims] and Jews . . . because the Lord prayed for those afflicting him, saying: ‘Father, forgive them for they know not what they do’. In this blessed house is powerfully fulfilled the heavenly doctrine: ‘Love your enemies and do good to those who hate you’; and elsewhere: ‘Friends should be loved in God and enemies on account of God’." --see Riley-Smith, pp. 21
In addition, people who spent long periods of time amongst non-Europeans in the intercrusade periods tended to become much more ethnically and religiously tolerant (go figure), which appeared strange to newcomers to the Holy Land. While I am not aware of any specific instances from the historical record, there certainly could be circumstances where a close-knit group of warriors, especially those with Hospitaller ties, would have consisted of various nationalities, including Arabs, Berbers, or other non-Europeans.
Most of this info is from a thesis I wrote several years ago, for more specific information check out: Hospitallers: The History of the Order of St. John by Jonathan Riley-Smith
Or try the best book about the crusades I've ever found: God's War by Christopher Tyerman.

They weren't that diverse. Well, they had members from most of Europe, including the Swedes, Germans, French etc., but that's about it as far as diversity. If you're thinking of the African that was with them, they never explicitly say that he was a Crusader. For all we know, he might have just been one of Balian's father's companions.