Short Answer
Saladin is believed to have spoken Kurdish, Turkish and Arabic. When communicating with crusaders, he needed an interpreter unless he was speaking to a crusader who knew Arabic (and there were certainly some who did - see examples below). I can find no evidence that he was conversant in any European language, though that does not mean to say that he didn't pick up a few words of Latin or Norman French.
Details
On Saladin's knowledge of languages,
The study of the Quran as well as the hadith would have given him
an excellent knowledge of Arabic, for although by birth he was a Kurd,
his education and learning would have been arabised at a very early
age. Nevertheless, it is likely that he spoke Kurdish at home. He
would also have equally been fluent in Turkish, which was the language
of the military.
Source: Abdul Rahman Razzam, 'Saladin' (2009)
His need for a translator when communicating with crusaders is evident in the aftermath of the Siege of Acre in 1191 when Richard I (for reasons which are unclear) massacred several thousand Muslim prisoners:
On hearing of the massacre Saladin was moved to fury....a day after the massacre a knight - 'his appearance announced
that he was a leading man among them' - was captured and brought to
Saladin. Through an interpreter, he was asked about the state of
Richard's army and then as to why the massacre of the Muslims had
taken place. The Knight replied that it had been the will of the king
of England. Saladin then ordered that the knight be put to death, and
when this was translated to him, he visibly blanched and requested
that he would free a Muslim prisoner in his place instead.
Source: Abdul Rahman Razzam
One crusader who was conversant in Arabic and spoke with Saladin was Reginald of Sidon. He communicated directly with Saladin during April 1189 when the sultan was camped with his army while besieging Beaufort Castle in southern Lebanon.
That there were crusaders and local Christians (as C Monsour points out in his comment) who spoke Arabic is not in doubt. One example was Humphrey IV of Toron, from the Kingdom of Jerusalem:
By the 1190s the balance between the Muslim world and Western
Christendom was very much in the Muslims’ favour. They were in the
ascendant in the ‘crusading’ wars, which, of course, they won with the
eviction of the Franks from Palestine in 1291. Theirs was also the
dominant culture. Communications across the linguistic divide were in
Arabic; the negotiations between Richard and Saladin’s brother al-Adil
were conducted through the young Humphrey IV of Toron, one of the
Franks fluent in the language.
Source: G. Hindley, 'Saladin: Hero of Islam'
Some of the Christians who spoke Arabic were descendants of earlier crusaders who had been on the First Crusade (1096-99). Although the large majority of those who survived that crusade returned home, some remained in Jerusalem and other settlements in the eastern Mediterranean, as did some of the pilgrims who had accompanied them.
