TO MR. OWENS AND ALL READERS OF THIS POST: I have just done some research work, thanks especially to the data supplied by Mr. Owens, that John Francis owned land in Mansfield, and, now find that John Francis is indeed shown as a resident of Mansfield, in the 1860 U.S. Census, and both his wife, Ellen, shown as being born in Australia, in about 1840, and his first two children (the other two were born in 1862 and 1865) are shown living with him.
So I wish to advise that my assumption, that John Fearn and John Francis were two entirely different persons, was totally incorrect, and I would like to apologise to one and all.
It is very obvious now that John Fearn had indeed moved to Louisiana from Australia, with his wife, sometime prior to 1856 (before the birth of his first child, as both children shown in the 1860 census were born in Louisiana), and John had adopted the surname of Francis, for some reason. There is an indication that he had married Ellen in Australia, in 1852, but so far I have been unable to locate a marriage listing in the indices, so they may in fact have eloped, as she was only 11 in 1852, and no doubt a marriage at that age would not have been permitted.
So thankfully, the 1860 census page has indeed confirmed that John Fearn and John Francis were the same person, and I shall be passing this confirming evidence to the descendant in Melbourne.
Once again, I do apologise to all for the incorrect assumption, and I thank you, Mr. Owens, for the lead which was able to provide the confirming evidence from the census record.