As far as I know the LaFranca family I am tracking is from Palermo, I am just starting and do not know the region well so maybe this is close to Particino? I need to study the regions. The reason I reply is that I also see that you posted for Imperiale. I have a LaFranca that married an Imperiale in my search. Benedetto LaFranca born 1899 died 1982 married a Nuncia Imperiale had kids Pietro and Ninfa I believe.
Francesco LaFranca b. 1821 d. 1887 Pietro LaFranca b. 1857 d. 1932 Marco Antonio Salvatore LaFranca b. 1893 d.1929 Vito LaFranca b.1891 d. 1970 these are some of the LaFranca names I am looking into. This information was from another family member and I have not verified any of it as of yet.
This line came to the US through Ellis Island and name was Americanized to LaFrank. Another name that ties in is an Infa Gerarda or Gerarda Ninfa? Unsure.