No hint as to his birth name. His father was named John and worked as a baker, per Charles' marriage certificate (his mother's name was listed as unknown).
On his naturalisation application Charles stated that he was born on the 6 December 1839 in Brest, France. The 1839 date lines up with the ages he provided on his children's birth certificates and marriage certificate. If we take that date as the absolute then either Eugene Perrot or Ulyn Gantier Ferdinand would be our best bet if Charles was one of those deserters listed in the Police Gazette. I would say that with the poor record keeping at that time the others listed still could potentially be Charles (beside Jean Marie Brun who was 28).
I forgot to mention earlier, family stories from multiple branches relay that Charles jumped ship (some branches mention a brother, others do not) - which is why I think that one of these men who deserted the Corneille could be Charles as it fits with the ship name he gave on his naturalisation application.
Charles' sons' names, which could possibly be a hint, were:
John Charles
Edward
Louis
Charles Alexander
Ernest Victor William
Henry Murray
Leonard Charles