There are many Quranic verses and Ahadith that talk about "jinns", but none of them speaks about their languages, but from some Quranic verses we can deduct that they can speak and understand the human language
قل أوحي إلي أنه استمع نفر من الجن فقالوا إنا سمعنا قرآنا عجبا
Verse 1 from Surat "Al-JINN "
Say (O Muhammad SAWW!): It has been revealed to me that a company of Jinns listened (to the Qur'an). They said, 'We have really heard a wonderful Recital!'
So we can deduct that they can hear the human talking.
قال عفريت من الجن أنا آتيك به قبل أن تقوم من مقامك وإني عليه لقوي أمين
Verse 39 from Surat " AN-NAML "
Said an 'Ifrit, of the Jinns: "I will bring it to thee before thou
rise from thy council: indeed I have full strength for the purpose,
and may be trusted."
In this Surah, the story of the prophet "Suliman" with the Jinn, and in this verse the Jinn speaks with the prophet "Suliman", so we can deduct either that the Jinn can speaks the human language or the prophet "Suliman" understood the Jinn's language .
So we can deduct that some Jinn can understand at least ARABIC language.
If you are familiar with ARABIC language I can suggest some good references.