a version of English or the language of the Anglo-Saxons

These are one and the same; Middle English - the language of Chaucer - develops fairly rapidly after 1066 from an amalgamation of Old English with the various French dialects left in England in the wake of the Conquest, including Breton, Picardy, Norman and even Occitan. In fact, the Old English of the Anglo-Saxons was essentially the anchor holding Middle English together as a language: as a result of the various French regional dialects and a move away from written English, Middle English abandons much of the grammatical structure and standardised spelling of Old English, leading to a sudden profusion of regional spellings and variation in the century after 1066. This amalgamation of language would have fairly rapidly become the everyday tongue of the English people; after all, it is at its heart Old English, just with a wide array of mutations and dialects.