Hello Kate,
I suppose your Maurice BALMA(I)N is the same as the one mentioned here:
http://archiver.rootsweb.ancestry.com/th/read/FRENCH-SURNAME... ? You might try contacting him to see if he found out more since then. ;)
The BALMAN (BALMANN / BALMAIN / BALMANE) surname is well known on La Reunion Island, see these pages (you'll find more on geneanet.org, try all spellings):
.
http://s169033694.onlinehome.fr/2010/08/04/louis-francois-de....
http://www.cgb-reunion.org/rfo07html/BALMANE%20et%20de%20BAL....
http://gw4.geneanet.org/index.php3?b=olivierauthier&lang...General infos about the "Ile de la Réunion" (previously "Ile Bourbon") and its history:
http://en.wikipedia.org/wiki/R%C3%A9unionNow, "La Réunion" being one of the French overseas departements (called DOM-TOM for short), its microfilmed archives are available both locally (at the Departemental Archives Center of La Reunion in Sainte-Clotilde) and on mainland France (at the ANOM = "Archives Nationales d'Outre-Mer" in Aix-en-Provence, and at the CARAN = "Centre d'Accueil et de Recherche des Archives Nationales" in Paris).
Unfortunately, they can't be found yet on-line (digitisation still on-going) and the centers do not reply to genealogical requests by mail. However, these archives were microfilmed by the LDS, so if you're living near a LDS center (
http://www.familysearch.org/eng/library/fhc/frameset_fhc.asp) you can try doing the research yourself by ordering a copy of the microfilm there. You'll find the references for La Reunion towns here:
http://www.cgb-reunion.org/mormons.htm Alternatively, you might want to join this yahoo group:
http://fr.groups.yahoo.com/group/GENBOURBON/ and post your question there.
Finally, you can also use one of these 2 free genealogical mutual aid services, they will just ask you to pay for stamps and photocopy fees if you want a paper copy:
Le Fil d'Ariane :
http://www.entraide-genealogique.net/index_outre_mer.php (wait till the La Reunion departement (974) is dark blue, otherwise it's unavailable)
FranceGenWeb :
http://www.francegenweb.org/~entraide/accueil_france.php (same, but the color expected is green)
The services are available right now, but read carefully the explanations for use first (on-line translator:
http://translate.google.com/#fr|en|).
And a last link for the road:
http://genealogy.about.com/od/france/a/french_ancestry.htm -> A Beginner's Guide to Researching Your French Ancestry
Hope all of this is useful and good luck!
Regards,
Amandine