Gabenesch and variant spellings in moselle

Dear Listers,
       This summer a man, whom I have been helping with his Genealogy is planning a trip to Moselle, especially to Amance in Meurthe-et-Moselle.
  Over the years I have helped several people with their German lines in this area of France. Here is my question and perhaps one of you can answer it. Is there a place, where I can write to find out, which civil registration offices in Moselle have listings of this surname or its variant spellings in their indexes during the 1800's? Perhaps, he can visit this office himself to do the research or have someone do some research before his trip to Moselle.
       Thank you for all your help.