Probably a lot of them were multilingual. Multilingualism certainly increased over time and there are plenty of examples of Europeans living in the crusader states who spoke various European and Middle Eastern languages. The crusades also led to increased study of foreign languages in European universities.

Most of the First Crusaders probably spoke similar Romance languages - dialects of northern French (Norman, Picard, Walloon), southern French (Occitan), and Italian, which were all still pretty similar to each other at the time, much more so than they are now (along with other Romance variants like Catalan, Castilian, Galician, etc).

But not all the crusaders spoke a Romance language. One of the chroniclers of the crusade, Fulcher of Chartres, noted the languages he heard from all over Europe:

“And whoever heard such a mixture of languages in one army? There were present Franks, Flemings, Frisians, Gauls, Allobroges, Lotharingians, Alemanni, Bavarians, Normans, English, Scots, Aquitanians, Italians, Dacians, Apulians, Iberians, Bretons, Greeks, and Armenians. If any Breton or Teuton wished to question me I could neither reply nor understand.” (Fulcher of Chartres, pg. 88)

So how did they communicate? Well we don’t really know, but presumably some of them spoke a Romance variant as a secondary language, or if they were clerics like Fulcher who had been educated by the church, they could have communicated in Latin.

When they reached the Byzantine Empire, there were lots of westerners serving as interpreters and translators in Constantinople. The Normans of southern Italy had been in contact with the Empire for decades already - sometimes friendly contact, sometimes unfriendly, as the Normans frequently attacked Byzantine territory. But that also means that some Normans in the crusader army might have spoken Greek.

One Norman crusader, Herluin, acted as an interpreter between the crusaders at the Seljuks during the siege of Antioch in 1098. Herluin could speak “their language”, although the crusader sources don’t seem to know what language it was - presumably Turkish, Persian, or Arabic. Maybe he had been to the Middle East before, or maybe he had picked up one of these languages in Constantinople…we don’t know for sure.

In the crusader states, plenty of languages were spoken there long before the crusaders arrived - Arabic, Greek, Hebrew, Armenian, Georgian, Coptic, Aramaic, and then they added at least French and Italian to the list. Some crusaders did attempt to learn Arabic, at least. For example, in 1187, when Saladin re-conquered most of the kingdom, Reginald of Sidon negotiated the surrender of Sidon - he told his troops to surrender in Arabic, so Saladin would understand him, but then told them in French to keep fighting. Some of the native Christian population probably also learned French.

“Had we been given the chance to walk through the bustling markets and streets of thirteenth-century Acre, we would have been struck by the great variety of languages used. Other than French, which was the dominant language spoken in the city, these would have included Provençal, various Italian and German dialects, English, Arabic and Greek…the composite character of the Latin East’s population and its mosaic-like structure resulted in a plurilingual situation in which different linguistic communities shared a given territory with only a small number of people serving as intermediaries.” (Rubin, pg. 62)

The network of intermediaries was already pretty ancient when the crusaders arrived, so that meant that even though there were always a stratum of people who could speak two or more languages, it was easy to find an interpreter or translator and not everyone needed to be multilingual. They even borrowed an Arabic word for “interpreter”, which they pronounced “dragoman”:

“This title is a corruption of the Arabic tarjuman - or interpreter…From the first, the Frankish lords would have needed interpreters to transmit their commands to their Arab villagers; and there already existed an established officer, the mutarjim...” (Riley-Smith, pg. 15)

Meanwhile, the presence of crusader states in the eastern Mediterranean helped spur interest in learning eastern languages in Europe - partly for communication and diplomacy, especially after the Mongols arrived in the Near East as well, but also for missionary activities. The Latin church eventually realized that crusading was a pointless waste of time and energy since they pretty much always failed. Maybe they should send peaceful missionaries instead, to convert people by preaching? Preachers and missionaries, mostly from the new Dominican order of monks, studied languages in universities in Europe and through immersion in the east. (Preaching didn’t work either…but at least this helped promote language-learning back home.)

There is a lot of academic interest in this topic, so here are some sources and further reading that are hopefully accessible:

Fulcher of Chartres, A History of the Expedition to Jerusalem, 1095-1127, trans. Francis Rita Ryan, ed. Harold S. Fink (Columbia University Press, 1969)

K.A. Tuley, “A century of communication and acclimatization: Interpreters and intermediaries in the Kingdom of Jerusalem”, in Albrecht Classen, East Meets West in the Middle Ages and Early Modern Times (De Gruyter, 2013)

Hussein M. Atiya, "Knowledge of Arabic in the crusader states in the twelfth and thirteenth centuries", in Journal of Medieval History 25 (1999)

Albrecht Classen, Multilingualism in the Middle Ages and Early Modern Age (De Gruyter, 2016)

Jonathan Rubin, Learning in a Crusader City: Intellectual Activity and Intercultural Exchanges in Acre, 1191-1291 (Cambridge University Press, 2018)

Laura K. Morreale and Nicholas L. Paul, The French of Outremer: Communities and Communications in the Crusading Mediterranean (Fordham University Press, 2018)

Jonathan Riley-Smith, “Some lesser officials in Latin Syria”, in The English Historical Review 87 (1972)