Since sources (including Geopatronyme) show that the Chenot name is found so strongly in Lorraine, I think this is a reason to consider it as the place first for your research. Lorraine and Alsace are very different, but the regions share a common history of suffering from German aggression during various times in history.
Also since Chenot is a such a good French name (and not at all Germanic), this is another reason to think of France first. If your grandparents spoke the French language, or a dialect such as Francique (Platt Lorrain / Lorraine Franconian), instead of German, this almost guarantees it.
This is simply something to consider.
Boone chance ! Good luck to you !