Where does James say he was born in the Censuses?
It's possible his father, (and/or mother) was still alive, at least by 1841.
Have you tried to track them down?
What about their burials? Have you found these?
They may have moved around Leicestershire, and not be buried in the village they were born in.
What about siblings of James?
Do you know of any? have you tracked them down in the Censuses? Where do they say they were born?
Perhaps one of the witnesses at his marriage was a brother or sister.
As california dreamin has mentioned, look at family naming patterns.
What were the children of James and Jane named?
And the children of any siblings.
Wills have also been mentioned.
These can be one of the best providers of genealogical information.
It was not always what we would consider wealthy people who left wills.
As well as looking for Goodwin wills, look also for any from Jane's side.
Her father may have left bequests for her, and his grandchildren.
Don't just look for any who you think might be their fathers - maiden aunts and bachelor uncles also often left bequests to their nephews and nieces.
And yes, you are correct.
It's never a good idea to base your family history on 'loose assumptions'.
"The Genealogical Proof Standard" says, "The three primary standards of proof are proof beyond a reasonable doubt, preponderance of the evidence and clear and convincing evidence."
Google it for more information.
By the way, I'm not sure why you've put "(GRO)" in your heading.
You will need to look at Censuses, wills, and pre 1837 records in parish registers, not the GRO.
You will need to use sites like familysearch.org, (free when registered and signed in), FreeREG.org, findmypast and ancestry. Leicestershire wills are on findmypast evidently.