Well, here's the thing: "Saracen" is a European construct. It has no real meaning. To the Europeans, a Saracen was basically any Muslim in the greater Levant region (or basically the modern Middle East). The Europeans similarly used the term Moor very broadly in the west (especially in Iberia; Morisco, the term of Spanish Muslims, just means "Little Moor").

But let's talk specifics. During the Third Crusade, Emperor Barbarossa decided to march to the Holy Land instead of trying to arrive by boat. This necessitated crossing Anatolia, the majority of which held by Turkic peoples. The most notable of these was the Sultanate of Rum (Rum referring to Rome, not, uh, rum), which was the principal successor state to the original Seljuq kingdom and was ruled (at least initially) by Seljuqs. Barbarossa's route involved carving a bloody path through Turkic land, including sacking the capital of the sultanate (Iconium or modern day Konya, located in south-central Anatolia).

The Seljuqs were ethnically Turkish, but they had something of an infatuation with Persia. Just like leading Romans of the Western Roman Empire liked to speak Greek to show how cultured they were, leading Seljuqs often spoke Persian (it eventually became the administrative language, too). While the Sultanate never included ethnically Persian land, that kingdom certainly had a very distinct Persian flavor to it. It's unlikely that your average run-of-the-mill guards would've spoken Persian, though.

But outside of Barbarossa's ill-fated expedition, most of the fighting in the Third Crusade revolved around the various Christian powers fighting the Ayyubid dynasty under Saladin. And Saladin's army was rather diverse.

The Ayyubids were based out of Egypt first and foremost (Saladin's Egyptian territory roughly corresponds to modern Egypt's borders). But Saladin raised troops from across his empire: Syria, northern Iraq, basically the entire western coast of the Arabian peninsula, eastern Libya, and most of the Holy Land. Saladin's armies, therefore, would've included Kurds, Egyptians, Arabs, Syrians, and various auxiliaries from less populous peoples (like the Bedouins). We know for a fact that Saladin himself spoke Kurdish as well as Arabic. Egypt also had a long tradition of employing slave-soldiers from Turkic peoples (the Mamluks, who would eventually come to rule Egypt). These people almost certainly still spoke some Turkic language(s). Since they were hired largely from the Caucasus slave markets, it's entirely possible that there were Mamluks of Caucasian descent as well.

Saladin also had a rather large number of Christians subjects. Arabic hadn't quite swept over Syria yet, so those Christians were likely to speak Aramaic. It's very likely that he also employed Nubians (people from Sudan), who spoke their own language. This was also two or three centuries prior to when the Nubian kingdom collapsed and Islam spread to the region, so they were almost certainly Christian as well. There were also a number of Jews living in the area, but I couldn't find any evidence to suggest they fought for the Ayyubids in any meaningful numbers. Granted, I didn't look very long.

All of which is to say that Saladin's army was ridiculously diverse. Moreso than the Crusaders, in fact.