Quite a few family trees have Charles Franks as born in Brest on 6 December 1839 with father Johann Jacob Frank (born in Speyer, Bavaria) and mother Maria Sybilla Heintz. Johann is of course German for John, so partly ties in with you knowing his father was called John.
Unfortunately that began with me. Charles' parents being Johann and Maria was a theory I had a while ago which I added to my tree so I could fill it out. Other people began copying it to their trees despite it only being a theory, so now it is present in many trees.
I can't find a Charles William P Franks born in December in Brest. Have tried various permutations including French variants of name.
Charles William P Franks came from an online cemetery register - I contacted the cemetery directly and they found that the register had been incorrectly transcribed. Charles Franks was what was in the register and "William P" part of the entry in the next register.
In saying that, Charles was referred to as Charles John Franks in his wife's death certificate - their son-in-law was informant.
Do you know for sure that your Charles is a deserter from the French Navy or are you just trying to work out how he got to Australia? There are lot of other migration records for people called Charles Franks. Too common a name to be sure of any of them, I'm afraid.
The family story is only that he jumped ship - it was never specified whether that be a Navy ship or a passenger ship. The Corneille fits as it comes from his own account in his naturalisation application. I've had a look at passenger ships that arrived in the 1860 - 1865 period but none have a name that resemble "Corneille".
There was a ship that arrived in 1862 called "Alfred the Great", three men deserted at Sydney - but I believe from the newspaper articles that they were apprehended.
They were:
Charles Frank, 25 from Lisbon
Manuel Domingo, Portugal
Francis Hanz (Also written Frank Hans), 22 from France
I think potentially Charles Frank or Francis Hanz could be my Charles Franks.
Unfortunately, I do think that for the most part these will only remain theories unless I get a DNA match that links to that side.