In the first crusade, contingents "naturally" split themselves into nations, even the the militant orders were to some degree split among linguistic lines (see e.g. the Langues of the Knights Hospitaliers). Later on, Conrad the 3rd's force was primarily composed of German speakers.
As French (languages (d'oc, d'oil...) was experiencing its first period as language of the elite (1100-1400) throughout Europe, e.g. Norman French in England (but also in Sicily!) besides Normandy and these Normans themselves were possibly the most numerous group (or 2nd, after the southern Provençal French) in the 1st crusade, Antioch becoming primarily Norman, some of the port cities (Acre?) being more populated by Provençals. For this reason, Old French was the main language spoken not just between the Crusader leadership but by most other members. Richard the Lionheart for example spoke French (but 6 months of his life ever spent on the isle of Britain!) The Assises of Jerusalem were even written in (Old) French, the legal code of the Kingdoms of Jerusalem then Cyprus.
(This is where the phrase "lingua franca" possibly comes from, the Arabs called these Europeans as a whole Franks. Although Lingua Franca/Sapir itself was primarily a language of trade and sailors, with its high point taking place centuries later.)
Now of course, there were large German speaking contingents too and many sailors and merchants were Italian (, Genoese, Venetian... or Armenian for the merchants, besides the Arabic of the majority of the local population (Aramaic having long since replaced Hebrew the language of daily life, itself then supplanted by Arabic)).
Latin of course remained eminently important as a literary and liturgical language, Gesta Tancredi being written about the Norman leader of the principality of Antioch, for example.
As Julie Barrau shows, medieval texts only rarely specify the language a conversation was held in, requiring us to make presumptions based on the class and origin of the speakers in question. And generally speaking, we only have sources speaking about the nobility/wealthy, so.
As she additionally makes a rather convincing argument that even in monasteries a strong command of Latin wasn't a given, we can presume many members of even the crusader leadership to not been capable of speaking Latin.
It's furthermore very important to remember that by German, French, Italian etc. the modern forms did not exist at the time, nor even single ancestor entities. Even by the French revolution only 1/8 of France spoke French: https://books.google.com/books?id=jKX1TenIOH0C&printsec=frontcover&dq=Sur+la+necessit%C3%A9+gregoire&source=bl&ots=3hG3zAtBfF&sig=7aqGkOkwSlxt3wRG-3mp4TMDbSg&hl=en&sa=X&ei=1p5MUOGZLoWa9gS_sYHoCQ&ved=0CCwQ6AEwAA#v=onepage&q=Sur%20la%20necessit%C3%A9%20gregoire&f=false
2.5% of Italy by unification: https://books.google.com/books?id=CswFBAAAQBAJ&pg=PA75&lpg=PA75&dq=tullio+de+mauro+2.5&source=bl&ots=6ZXeW8tbS6&sig=QAKtmxsCwbQueQG625lchod2CgA&hl=de&sa=X&ved=0ahUKEwih1K6nkt3TAhXH6iYKHe62AG8Q6AEILzAC#v=onepage&q=tullio%20de%20mauro%202.5&f=false