I'm sorry but I don't have a gift to you read your mind. You did not mention one word about what you ordered and read through at the archives... I am amazed that you think a anonymous Internet contact who has received a Twitter-length message can give you better advice than the excellent flesh-and-blood archivists at the Archives départementales (AD Moselle) in front of you!
First, did you show your document that says « Forbach » to an archivist? What advice did the archivist give to you?
What do you mean « cannot find the commune »? Does this mean you can't find any records for Forbach in AD Moselle? (Did you ask if they were destroyed during the First World War?) in this case, you may have to drive to Forbach city hall to see their second original copy. --- Or does it mean the names of your family members do not appear in the tables décennales for Forbach at the archives?
Did you look through lists of the « Optants » that show who registered to keep French citizenship and who took German citizenship after the occupation in the 1870s?
Did you look at the Annuaires de Commerce (« Bottins »), similar to City Directories, for the years your family was in France? (For some places, such as the city of Nantes, they go back to the 1750s, and may be organized by occupation, address, and/or by name.)
Did you ask archivists about any name indexes they might have available, for example, those they may have prepared by past researchers or genealogy societies like those at many other archives, if any. (I don't know what AD Moselle has, but many Archives départementales have them sitting on their book shelves.)
(By the way, I hope that before you arrived at AD Moselle that you searched for your families on the biggest French genealogical databases at GeneaNet and Généalogie.com.)
For a next step, consider visiting a local genealogy society which should have indexes prepared by members that are often excellent. The biggest society is not far from you: Cercle Généalogique de Moselle ~ 1 allée du Château ~ 57070 SAINT-JULIEN-LES-METZ, Tél : 03 87 78 05 31, les mercredi de 8h30 à 16h30 et samedi de 8h30 à 12h00 --- (Go today, or you will have to wait until Saturday.) People are always very helpful at these places. Here is the website: http://www.moselle-genealogie.net/
I hope you are enjoying Metz, the new museum, and the many sights in the historic city.
Bonne quête !