The first step would be identifying which town your relatives came from precisely, either from US censuses or ship manifests.
For US immigration, you can use these:
Then for a list of French genealogy links, see my message here (scroll down if needed): http://boards.ancestry.com/localities.weurope.france.general...
Corse is divided into 2 departements with each its own archives. Also, some big towns, like Bastia or Bonifacio, have kept their set of archives (civil registry and/or parish registers) and put some documents or archives on-line on their own.
- #2A : Corse-du-Sud (South, formerly called Basse-Corse): http://en.wikipedia.org/wiki/Corse-du-Sud
-> Departmental archives website: http://www.cg-corsedusud.fr/patrimoine-et-culture/archives-d...
Vital records have been digitalized but are not yet available on-line.
However you can already search the military service records for men from 1859 to 1918: http://www1.arkhenum.fr/ad_corsedusud_matricules/
-> Bonifacio municipal archives: http://www.bonifacio-mairie.fr/corse-du-sud/bonifacio.php?me...
All records are to be downloaded as PDF files. Can be found there: 1814 census, parish registers for Sainte-Marie from 1682 to 1814 and births, marriages, deaths from 1797 to 1800.
- #2B : Haute-Corse (North): http://en.wikipedia.org/wiki/Haute-Corse
-> Departmental archives website: http://www.cg2b.fr/cg2b/cgi-bin/pages/index.pl?lang=fr/&...
All civil registry from 1793 to 1902 has been digitalized but only the first quarter (for towns from Aghione to Pigna) is on-line for now.
. naissances/mariages/décès = births/marriages/deaths
. publications de mariage = marriage banns (recorded in both the groom and bride home-towns)
. tables décennales = 10-years indexes (alphabetical and/or chronological)
-> Bastia municipal archives: http://www.bastia.fr/rubrique.php?id_rub=archives_etat_civil
You'll find there transcriptions (= lists of dates & names) of Bastia parish registers: births (1763->1804), baptisms (1707->1795), marriages (1765->1804), deaths (1750->1805) as well as 10-years indexes (tables décennales) for the period 1893/1932.
/!\ These 2 last websites refused to work well with my Firefox browser, so try Internet Explorer if you get the same trouble.
One last tip: don't forget to check all possible spellings (especially on Geneanet). For example, the variant Giuli seems much more current than Guili. ;)
Hope that'll help you a little. Good luck!