Hi eveder,
Interesting that the children of John and Frances seem to stop before the marriage of John and Elizabeth - this adds further credence to the theory that the two Johns are the same person.
I don't think the St. Andrews Holborn records will help you as it is usually baptisms that are recorded, not births (you just got lucky on the Old Church Saint Pancras baptism record that they also took the time to also note her date of birth). And that record does not say she was born in St. Andrew - that is only from the census. I wouldn't take that as gospel truth. London birthplaces are notoriously wrong on the census.
I would order the Old Church Saint Pancras records (or request a look-up here on Rootschat) to check the original that the IGI record came from, in case there is more information noted. When I went back to the IGI, I also noticed that her marriage record is there!
Frances Palmer Smith and Samuel Goss, 10 Dec 1854 Old Church Saint Pancras.
So, if someone has access to the records, they might be able to look that up for you at the same time they are looking up Frances' baptism. Or you should be able to find them in the BMD index and order their marriage certificate.
I can't find Frances and Samuel in the 1861 to see what she says as her birthplace.
The Saint Andrew Holborn records are on the IGI, so if you want to have a look you can. But I don't see any likely candidates - I also checked for Frances Palmer with a different last name, but there are none.
If Frances' baptism and marriage do not help you, then I think your next step will be to check the original versions of the two John Smith marriages, to see if there any clues that can help you determine if they are the same person...
It may be case of John deciding to name her after his father's first wife, for some bizarre reason!
MJP