The Eyres (Ayres, etc) families do go back quite a ways, but tracing back to the Conquest is a bit of a reach. The pun that "makes" the "family legend" works *only in English*.
Surname Database gives several possible derivations (they are not consistent between the A and E forms, nor between the ones with and without a terminal S). "Eyre" they claim to be Old Norse and locational, probably from Cumberland, deriving from "the Old Norse term "eyrara", meaning "gravel-bank stream or river"." http://www.surnamedb.com/Surname/Eyre
Other derivations given under other variants:
* "a nickname for a man who was well known to be the heir to a title or fortune, deriving from the Middle English "eir, eyr", a development of the Old French "(h)eir" meaning heir";
* a locational surname from a place called Ayr in South West Scotland, deriving from the Old Norse "eyrr" meaning tongue of land, gravelly bank, plus the suffix "s" denoting of "the place";
* a patronymic form of the Middle English personal name "Aier, Aer", itself coming from the Olde English pre 7th Century "Ealhhere", a compound of the elements "eal(h)", old, and "heri", army
http://www.surnamedb.com/