* Great-grandmother on the mother's side: arrière-grand-mère (pronounced "ar-ree-er grã-mer")
* Great-grandmother on the father's side: grand-mère paternelle (pronounced "grã-mer pa-ter-nel")
While "arrière-grand-mère" is the most common and neutral term, "grand-mère paternelle" is more specific and directly translates to "paternal grandmother".