I have encountered the name Istorique Bédard and it remains mysterious.
The father of Isaac Bédard (the first Bédard in New France) was Jacques Bédard in Aunis, France. Check this link http://genealogiequebec.info/testphp/info.php?no=60995
it goes back to before 1460.
Hope that helps!and good luck with the search for Eliza Peters