This is great, thank you both.
Conscious you're travelling some of the ground I've covered - but finding some new things! (especially that 1828 passport for Francis) - let me give the background which I should have done first, apologies.
Taking a couple of steps back, my own focus is John Peter Gassiot, eldest surviving son, 1797-1877, a notable figure in Clapham, where I'm based. Am pretty confident about him / well researched.
I've also researched his mother, Harriet Dixon (B, M and D, probate etc) and his father John Peter Gassiot (only M, not birth in ?Fr/Sp, nor death ?here). I've found lots on his various failed wine import businesses, his move to Edinburgh perhaps to avoid creditors, and am guessing he died around mid 1820s (nothing found on that).
Their children were:
Peter b1796, presumed death before 1799
John Peter as above
Peter 1799-1862, life fully researched (Royal Marines, marriage, children, etc including his adoption of a family name on his mother's side)
Then there is Samuel, b1813 Edinburgh - ?died, a real mystery
and also two children cited in the original American research -
Marie, claimed birth 1801, no source cited, no records found
and Francis who went to America where there's an extended family.
Those catholic baptisms feel highly significant and explain the absence of the usual parish records except marriage (Samuel in Edinburgh is the outlier.) A baptism for Francis c1802 onwards would be a major breakthrough. I've trawled every single entry in the RC St George's register (hence found the earlier Peter one, mistranscribed).
There is an entry record for Francis in November 1828 into Philadelphia (no age) and lots in American sources thereafter, including this passport application from 1836 (no age):
https://www.ancestry.co.uk/imageviewer/collections/1174/images/USM1371_1-0081?pId=1117654There's also a New York entry record in 1833 where the cited age implies birth of 1804.
The 1828 passport application feels very significant and is not mentioned elsewhere as far as I know.
Hope that puts things into context and explains my focus on Francis and that strange reference to 1816 (and the claimed birth date as 1809).
At risk of overwhelming you, here's a write up which the family in America have of their origins. It's a mixture of facts and if not fiction, then misunderstanding and surmise.
http://freepages.rootsweb.com/~gassiot/genealogy/history/roger.htmYou can see the problem. So I'm trying to bottom out the English (and now Scottish) components. Tricky enough, before embarking on France and Spain. The American end looks well worked over, albeit differing names and dates.
Anyway, thanks again, keep the ideas coming - it's a tough one!