This region has moved back and forth between French and German rule over the centuries. The North American continent, especially the United States, has welcomed many emigrants from Alsace Lorraine.
Chronology of Alsace and Lorraine Jurisdictions
Before 1648: Alsace is part of the Holy Roman Empire.
1648: Most of Alsace becomes part of France.
1766: Lorraine becomes part of France.
1871: Alsace and part of Lorraine ("German Lorraine") are annexed by Germany under the name Elsaß-Lothringen. Bismarck takes from Napolean III the French départments of Bas-Rhin, Haut-Rhin, and Moselle. The western part of Haut-Rhin becomes the territory of Belfort.
1919: Alsace becomes part of France, following World War I. (The old Alsatian départments of Bas-Rhin and Haut-Rhin are restored. The Lothringen section becomes the départment of Moselle.)
1939-1945: Alsace becomes part of Germany during World War II.
1946 to present: Alsace is part of France. (Alsace takes in the departments of Bas-Rhin, Haut-Rhin and, since 1871 the Territory of Belfort; Lorraine corresponds to the departments of Moselle, Meurthe-et-Moselle, and parts of the départments of Meuse and of Vosges.)
For your reference, here is a general Map of Alsace Lorraine: