In the first of her surviving letters to Abelard, Heloise wrote:
You had, besides, I admit, two special gifts whereby to win at once the heart of any woman — your gifts for composing verse and song, in which we know other philosophers have rarely been successful. This was for you no more than a diversion, a recreation from the labours of your philosophic work, but you left many love-songs and verses which won wide popularity for the charm of their words and tunes, and kept your name continually on everyone's lips. The beauty of the airs ensured that even the unlettered did not forget you; more than anything this made women sigh for love of you. (translated by Betty Radice)
From the fact that "even the unlettered" enjoyed these songs, we know that they were written in Latin, not in the vernacular (as were the songs of the early troubadours from around the same time). Interestingly, Abelard grew up in Le Pallet, which lay in northern Poitou — and it was in Poitou that the art of the troubadours was born: the first of the troubadours was William, Count of Poitier (1071–1126), followed by Jaufre Rudel (fl. 1125–1148) and Marcabru (fl. 1129–1149). Abelard's father was a successful knight and a Poitevin, perhaps bound by fealty to William of Poitier, so it is possible that the young Abelard went to William's court in Poitier before he left to study outside Poitou in his teens sometime in the mid-1090s.
Unfortunately, Abelard's secular songs have been lost to us, although some of his later sacred songs survive (a fine rendering of his Planctus David can be heard on Paul Hillier's recording Troubadour Songs and Medieval Lyrics). Some scholars have speculated that since Abelard's love songs were so well-known at the time it would be reasonable to think that some of them have been transmitted to us in collections such as that found at the monastery of Benedictbeuern early in the 19th century (a collection that has become known as the Carmina Burana). I too find this an attractive thought, although it is impossible to know which of these poems might have been composed by Abelard. That has not stopped people from trying, however. I hope to add translations of likely candidates soon.