I would say, based on the baptismal record for a John Carter, on the 29th September 1678, in Irchester, Northamptonshire, that his parents were more probably John Carter and Mary ?
More than that I could not tell you.
(I updated his marriage date to that from the records. The date that was on the profile was one of the readings of the Banns, and did not match the source stated. I also removed duplicated text, and headers, and removed the <ref>tags</ref> from beneath the Sources header.)