Deb, I suspect Nicolas was born in France, most likely in the Alsace region. There are a lot of Nicolaus Bauers listed on the IGI.....but no connection to Joseph that I can see.
The Horse Dealer bit has me intrigued......
......dee
Coming in very late to this one, Part 1 started before I was aware of Scavenger Hunts

...but looking at Nicolas, if your man is a Horse Dealer, this could well have an Irish connection to it somewhere along the line, even if it's only that he was there on business.
I know the Irish Censuses have gone down the tubes, but might there be anything else in the archives? details of businesses, owners of stud farms and their day-to-day paperwork?
......................
If I remember rightly from all I have read today in Part 1, there is a Hugh b. c1824 Belfast (Perfumier), Francois b. 1827 France/London (Cook), Joseph Jnr. b.c 1829 Paris (Cook), Louisa Isabella chr. 1833 (Cook) - and George b. 1848 by Emma Mansfield (she m.Joseph Snr. 1846 Hammersmith) and we are trying to get the link, esp. between Francois and Hugh.
Hugh would be the eldest
if these were all siblings, but so far, the only confirmed children of Joseph Snr. are Francois, Louisa & George - Hugh & Joseph Jnr. being likely but no proof yet - and Joseph Snr's father is Nicolas, but no siblings yet for Joseph Snr.
Have I got this right?
I'm missing one bit though - do you have a place of birth for Joseph Snr?
(note to me so I don't lose the plot

: Joseph Snr. b. c1796 d. 1853, occ. Cook, m. to Isabella, then Emma)
I had a look at the photos, the resemblances are remarkable. I transposed pic. bottom left so he was facing same way as pic. centre top - not much doubt on visual evidence, you just need the proof...

...and I had a look at the Joseph Snr./Isabell entry in the reg. entry that was posted up, her surname looks like Leoppold or Leoppard, suspect the former.
I'll make a start on seeing if I can find anything new...