Anna Komnena called Bohemond a Gaul several times in the Alexiad. I have to think the term is pejorative. However, I only read the English translation, never the Greek so there's always the possibility of translator bias or nuance.

That said - the Alexiad is an interesting source from the viewpoint of the daughter of the Emperor of Byzantium.

Then there's The Chronicles of the Crusades by Joinville and Villehardoin. That one is still on the shelf.

Initially, Byzantine hopes were pinned on a Frankish influx of manpower to turn the tide against the threatening Turkomen powers to their east. However, once the Franks arrived, they ended up proving just as threatening to Byzantine stability. Eventually they'd end up sacking Constantinople in the Fourth Crusade!

The First Crusade is interesting, as even William of Tyre, a fairly pro-Crusader source writing at a century or so's remove from its events, is keen to observe the rampaging character of the so-called "People's Crusade" led in part by an itinerant preacher, Peter the Hermit. These generally landless and impoverished crusaders swept through Germany and Eastern Europe killing Jews and swallowing up countrysides full of grain and supply before moving on, like anti-semitic locusts. By the time they arrived in Byzantine territory the Crusaders actually managed to come to blows with their ostensible allies!

Eventually all who took the overland route swore to the Emperor they would return any captured territory to his empire. Most had no such intention. Bohemund and Tancred, leaders of the Antiochene Crusader state that arose after the success of the First, actually fought the Byzantines almost as much as the "Saracens," both before the Crusade and, indeed, sometimes after.

The Byzantine Emperor even imprisoned Hugh of Vermandois in 1096 because he had reason to believe he was the vanguard of a conquering Frankish army. Hugh was eventually freed, but the Emperor was right in the main: the Crusade quickly changed from a spontaneous eruption of religious-military sentiment to a noble-led land grab with religious trappings.

There is a real irony to the fact that the First Crusade was allegedly sparked by the Emperor's appeal to Pope Urban II for help against the Seljuks- when the Crusaders arrived, many, including Peter the Hermit, had to beg military assistance from the Emperor! Moreover, the Seljuks were in no way displaced by the Crusaders and the Byzantines continued their journey into imperial decline.

Here's a bibliography for you. Good introductory sources are bolded and annotated.

Andersen, Per, Mia Swendsen, and Helle Vogt. Law and power in the Middle Ages : proceedings of the Fourth Carlsberg Academy Conference on Medieval Legal History 2007. Copenhagen: DJØF Pub, 2008. Print.

Armstrong, Karen. Holy war: the Crusades and their impact on today's world. New York: Doubleday, 1991. Print.

Ashbridge, Thomas. The Crusades: The Authoritative History of the War for the Holy Land. HarperCollins. Kindle Edition.

Babcock, Emily Atwater, and William of Tyre. A history of deeds done beyond the sea,. New York: Columbia University Press, 1943. Print. Tyre's work should be read with an eye toward its source's perspective and the limitations of the historian himself, but his work is an important starting point.

Barber, Malcolm. The crusader states. New Haven: Yale University Press, 2012. Print.

Ben-Ami, Aharon. Social change in a hostile environment: the crusader's Kingdom of Jerusalem. Princeton, N.J.: Princeton University Press, 1969. Print.

Claster, Jill N. Sacred violence : the European crusades to the Middle East, 1095-1396. Toronto Tonawanda, N.Y: University of Toronto Press, 2009. Print.

Harding, Alan. Medieval law and the foundations of the state. Oxford, UK: Oxford University Press, 2002. Print.

Holt, P. M. The Crusader states and their neighbours, 1098-1291. Harlow, England New York: Pearson Longman, Pearson Education Ltd, 2004. Print. This is an excellent, and very short, introduction to the layout of the Outremer and has some good introductory materials on Byzantine-Crusader relations.

Jenks, Edward. Law and politics in the middle ages with a synoptic table of sources. [2nd ed. London: John Murray, 1913. Print.

Ḳedar, B. Z. The Franks in the Levant, 11th to 14th Centuries. Aldershot, Hampshire: Variorum, 1993. Print.

Kohler, Michael, P. M. Holt, and Konrad Hirschler. Alliances and treaties between Frankish and Muslim rulers in the Middle East : cross-cultural diplomacy in the period of the Crusades. Leiden Boston: Brill, 2013. Print.

Prawer, Joshua, et al. Outremer : studies in the history of the crusading kingdom of Jerusalem presented to Joshua Prawer. Jerusalem: Yad Izhak Ben-Zvi Institute, 1982. Print.

Prawer, Joshua. Crusader institutions. Oxford New York: Clarendon Press Oxford University Press, 1980. Print.

Riley-Smith, Jonathan Simon Christopher. The Crusades: A History. London, England: Bloomsbury Academic, 2014. Print. Riley-Smith is the o.g. of Crusader Studies. This book is just a little, slim volume that has a lot to offer a new-comer. Give it a shot.

Smith, Jonathan Simon Christopher. The feudal nobility and the kingdom of Jerusalem, 1174-1277. Hamden, Conn.: Archon Books, 1973. Print.