Welcome to the most difficult part of Europe to research. For starters, "Alsace-Lorraine" is not one place and doesn't have a single source of records. It's like referring to part of the Midwest as "Wisconsin-Illinois". Alsace was the more German province and Lorraine was along for the ride during WWI. The problem you face is that they don't have a single archives for records, every province has separate "departements" like Vosges and Meuse or Meurthe-et-Moiselle. They are like counties in the US and they keep their own records in their own archives. Hartman is not a very unique name. But it's also not very French. Believing it's possible that it came from either province is realistic, but it's probably more likely from Alsace. What you need to do is go to the LDS and request the microfiche (different than the films) of the passport/visa requests from each departement in each of the two provinces. It's the only cohesive recordkeeping that's easily available in the US.From there, it depends on the year of emigration. Post-1850 is much easier to trace than 1789-1830. Also check the port of departure. If it was Amsterdam or Rotterdam, the records are in good order and kept by those magnificent genealogists in the Netherlands. They're the best at sharing information on the internet.From the 1790s to present you'll also want the Civil registers to track births, marriages and deaths. (Beware of the French Revolutionary calendar). Pre-1792 you'll also want to search Catholic parish records for births, marriages and deaths.There is no great website to search for French records, but
http://www.geneanet.org is pretty decent.