https://books.google.fr/books?hl=fr&id=FWkNAAAAIAAJ&dq=deslongrais+mauritius&focus=searchwithinvolume&q=deslongraisDESLONGRAIS Louis Marie Auguste Durand, 2d son of Henry DURAND DESLONGRAIS of Port-Louis, Mauritius, bar. at law. Born 1837.
So his father is a Henry DURAND DESLONGRAIS and he has two sons.
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Henri MAUREL, a specialist, mentions Louis Marie Henry DURAND DESLONGRAIS, as a son of Denis Louis DURAND and Marie JOCET DESLONGRAIS.
http://gw.geneanet.org/hmaurel?lang=fr&p=louis+marie+henry&n=durandMarriage in 1832 to Louise Julie Mimi GOUREL de SAINT PERN
He was born in 1805 in Port-Louis
http://anom.archivesnationales.culture.gouv.fr/caomec2/pix2web.php?territoire=ILE%20DE%20FRANCE&commune=PORT-LOUIS&annee=1805&typeacte=AC_NAFrame 25
Son of Denis Louis DURAND, notaire, and Marie JOCET DESLONGRAIS
(Notaire from 1791 to 1809
http://anom.archivesnationales.culture.gouv.fr/ir?num=20&referer=nominatif&q=&ir=FRANOM_00038&persname_authfilenumber=1248&start=1)
The death record of his sister Marie Joseph Henriette DURAND DESLONGRAIS in Dijon clearly shows that the family name DURAND DESLONGRAIS is the association of her father's name and half of her mother's name (nom de branche). They belonged to the bourgeoisie and there were other DURANDS on the island. DESLONGRAIS made a difference and added some prestige to a very common French name. It also indicates the maternal lineage (mother born on the island and certainly better known by the locals than a newcomer).
A long record describing a good part of their grandfather's carreer (Charles Malo JOCET DESLONGRAIS)
http://anom.archivesnationales.culture.gouv.fr/p2w/?dossier=/collection/INVENTAIRES/Ministeres/SEM/E/&first=241_349B/FRCAOM06_COLE_241349B_0677&last=241_349B/FRCAOM06_COLE_241349B_0876&title=Jocet-Deslongrais,+Charles+Malo,+ancien+commissaire+de+la+Marine,+et+sa+fille+Marie+Madeleine,+%C3%A9pouse+divorc%C3%A9e+de+Advisard+(Joseph+Guillaume),+capitaine+au+r%C3%A9giment+de+l%27%C3%AEle+de+France+1755/an+IIHenry DURAND DESLONGRAIS has at least one son, Louis Armand Charles DURAND DESLONGRAIS, husband of Marie Emma ICERY.
REPERTOIRE DES MINUTES DES NOTAIRES DE L'ILE MAURICE
https://www.cg974.fr/culture/.../418-10-J-et-1-MIANM-Notaires-de-l-île-Maurice.html
Etude DURAND-DESLONGRAIS. 1867-1891. Louis- ...... Pamplemousses. HARSCHER (Jean Henri) ... DURAND-DESLONGRAIS (Louis Armand). DURRANS ...
South African Commercial Advertiser 1842 - 2 - April to June - eGGSA ...
https://www.eggsa.org/newspapers/index.../53-sac-1842-apr-junTraduire cette page
In the Independent Chapel on Tuesday 22nd March by the Rev Henry ... by the Rev J Griffith, Adr. Louis Henry Durand DES LONGRAIS, of Mauritius, to Leontine ...
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On Findmypast, there is an entry for
Deslongrais Auguste D — — 1860 Index To Register Of Passport Applications 1851-1903 —
I can't see the record. Does it give some interesting details ?
There is also
Deslongrais Samuel D — — 1860 Index To Register Of Passport Applications 1851-1903 —
You said that Auguste DURAND DESLONGRAIS arrived around 1860 and his wife, Marie, gave birth to a daughter in 1860.
Is it because of her death certificate that you know Marie's maiden name ?
Deslongrais Marie 1824 1880 1880 England & Wales Deaths 1837-2007 Warwick, Warwickshire, England
Place of birth in the 1871 census ?
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The way I feel things Auguste is the second son of Louis Marie Henry DURAND LESLONGRAIS and his wife née GOUREL de SAINT PERN and a grandson of Denis Louis DURAND and Marie Joseph DURAND DESLONGRAIS.
As you couldn't find his birth record in Port-Louis, we can deduce he was born somewhere else (unless some records are missing).
If you could be sure of the maiden name of his wife Marie and her birthplace, maybe there is a chance to find their marriage record. Hopefully, they got married in France.