Figured it was something along those lines. Undoubtedly old Germanic (Angle and Saxon) in origin, when spoken with a sort of Scots burr it was quite a lovely sounding language.
As you will note, the selection from Chaucer does NOT contain case endings (except for those that have survived into Modern English). After the Norman Invasion in 1066, the Anglo-Saxon language was subborned to the native French of William the Conqueror and his cohorts. For this reason, The old Germanic Anglo-Saxon language was supplanted by Middle English (a combination of some A-S words, some Latin words, and many French words). Rather than a Scottish burr, it should be spoke with a French elision and vowels that do not change in pronunciation (we're before the great vowel shift that gave us multiple sounds for each vowel). "A" is ah, like in bawl; e is eh, like in wet; i is ee, like in beat; and so on.
The proper pronunciation of the first line from Chaucer would have been like : Wh-ah-n th-ah-t Ah-preel weeth hees shoh-wehrs sh-oh-t, etc (with vowels separated in my transliteration, but not in actual speech).
So, in reality, the thorn character was used in Anglo-Saxon (Old English), but was gone from Chaucer's dialect of Middle English by the time he wrote (but it still existed in some northern dialects of Middle English... like that of Sir Gawain and the Green Knight... but that's a whole other discussion)...