Thanks to several generous researchers in Canada, England, and France, I have been able to make some progress on the family of Archibald Kane (1775?-1817):
1. Archibald2 Kane (John1) died at Port-au-Prince, Haiti 27 September 1817 aged about 42.
By Jeanne Julienne Bonnet, who died at Port-au-Prince 29 November 1825, natural daughter of Marie Louise Lamanière, and wife (1820) of Louis Victor Nonez, Director of Customs in Port-au-Prince .
2. i. Marie Louise Isabella3 Kane.
3. ii. Louise Joséphine Adeline Kane.
4. iii. Jeanne Joséphine Kane.
2. Marie Louise Isabella3 Kane (Archibald2; John1) died at Toxteth Park, Lancashire, England in 1890. She married at Port-au-Prince, Haiti 24 November 1827, Robert Alexandre Windsor, who was born at Port-au-Prince 14 August 1808 and died there in 1850, son of Robert Harley Windsor and Marie Magdelaine Jouve.
The 1881 British Census lists Isabella Windsor, 72, a native of Port-au-Prince, living at 92 Durning Road in West Derby, Lancashire, with her grandsons Thomas Purgold, 15, a native of Port-au-Prince; Adolphe Purgold, 13, George Purgold, 11, and Leopold Purgold, 9, natives of Hamburg; and Robert Windsor, 7, a native of Calcutta.
5. i. Robert Jean Baptiste4 Windsor.
6. ii. Louise Alexandrine Clara Windsor.
7. iii. Jeanne Julienne Claire Windsor.
8. iv. Isabella Windsor.
9. v. Jean Baptiste Archibald Windsor.
10. vi. Nicole Joséphine Emilie Windsor.
11. vii. Thomas Windsor.
12. viii. Georges Windsor.
3. Louise Joséphine Adeline3 Kane (Archibald2; John1) died at Port-au-Prince, Haiti 23 February 1816 aged 4.
4. Jeanne Joséphine3 Kane (Archibald2; John1) was born at Port-au-Prince, Haiti 10 May 1813 and died there 26 May 1819.
 Acte de décès d'Archibald Kane, Port-au-Prince 28 September 1817.
 Acte de marriage entre Louis Victor Nonez et Jeanne Julienne Bonnet, Port-au-Prince 8 January 1820; acte de décès de Jeanne Juillette Bonnet (Veuve Nonez), Port-au-Prince 29 November 1825.
 Acte de décès de Louis Victor Nonez, Port-au-Prince 4 October 1825.
 Source to come from British records.
 He was legitimated by his parents' subsequent marriage. Acte de naissance de Robert Windsor, Port-au-Prince 22 October 1808.
 Family History Library film 134,1887, p. 31.
 Acte de décès de Louise Joséphine Adeline Kane, Port-au-Prince 23 February 1816.
 Her father, Archibald Kane, aged 40, was an American merchant; her mother, Juillet Bonnet, 29, was a proprietaire. Acte de naissance de Jeanne Joséphine Kane, Port-au-Prince 1 May 1815.
 Acte de décès de Jeanne Joséphine Kane, Port-au-Prince 27 May 1819.
I would also like to communicate with Peter Frisch, whose work on the Jouve family intersects with the family of Isabella Kane, Archibald's only known daughter (to me, at least).