I believe that I have found the identity of Charles Franks. There was a Jean Cloarec born 6 Dec 1838 in Boudouguen in Hanvec to Joseph Cloarec and Marie Catherine Omnes. He had three siblings that I have found so far, Marie b. 1841, Jean Louis b. 1842, and Joseph b. 1845. I had a French DNA match that showed up as a potential 4th cousin and I successfully connected her to Marie Cloarec b. 1841. On his marriage certificate Charles listed his father as a baker named John Franks, whereas Joseph Cloarec was a farmer. I will have to investigate this further but I believe that the DNA does connect Charles Franks to Jean Cloarec.
I suspect that the Jean Clorie listed in the "Seamen Deserters" article was mistranscribed from Jean Cloarec as the note to the paper would have been handwritten as typewriters did not become common use until the mid 1880s. I can see from looking at the name in French birth records that if you were unfamiliar with the name you may mistake the "ec" as an "ie".
Thanks to everybody for their help!