"Huron Carol"
Discussion, a link by Masato, the French words, etc. are found in thread 15332: Huron Carol
A brief summary here, in answer to Jack Campin. The 'Huron Carol' in the DT is nonsense.

The title, "Jesous ahatonhia," is commonly given simply as 'Huron Carol,' or 'Canadian Christmas Carol.' It was found in tradition with a small group of Hurons who settled at Lorette, Quebec, and Father de Villeneuve, SJ, sometime between 1747 and 1794, wrote down the words as he heard them.

By tradition, the song is attributed to Father Jean de Brébeuf, SJ, sometime before 1649; one of the five Jesuits, and three others, who were killed during fighting over the fur trade between the Iroquois and the Hurons. Jean de Brebeuf and the others were canonized as martyrs by the Catholic church. The Hurons at Ste Marie had to abandon the village and removed to Christian Island in Georgian Bay, where many died or were scattered. A few made their way to Lorette.

There are questionmarks about the history of the song. In a letter written back to Quebec, de Brebeuf mentioned a Christmas celebration by the Hurons, where hymns were sung. No mention of the carol. The Lorette Hurons spoke of a collection of Huron songs and chants assembled by Father Chaumonot SJ, but this record has never been found.
The words are sung to a tune from the French carol "Une Jeune Pucelle" (A young maiden), and in its opening is reminiscent of "God Rest Ye Merry, Gentlemen."

There are several English 'interpretations' set to music; I have a score in a book published for Canada's Centennial in 1967 by J. E. Middleton, but his 'interpretation,' the one in the DT, and given at the beginning of thread 15332 by Marion, is laughable. Masato gives a link to the version by Father H. Kierans, SJ, which is good, and linked properly to the music (other interpretations including Middleton's 'It was in the moon of wintertime,' also are in the link), in a 2005 post to thread 15332.
The song was apparently collected by Father de Villenueve in Huron version, and translated into French (or v. v.?). Barry T. gives the French text in thread 15332. The Huron is also given in that thread. McGrath gives an English translation which is reasonably close to the French and the Huron.
The link by Masato, however, is to the most reliable information.
No 17th c. text has been preserved.

The oldest North American religious choral music and hymns were composed in the 16th c. in Mexico, a number of them extended compositions (Masses) by excellent musicians. Some have been recorded recently.