Am I French or German?

I have been researching my ancestry recently and discovered that my ancestors who came to America were originally from the Alsace region of France. They left about 2 years after the Franco-Prussian War when Alsace was incorporated into Germany. In the 1880 census my 2nd great-grandfathers home country is listed as France, my 2nd great grandmothers is listed as being from Baden. In the 1900 census it says they are both from Germany. I also understand that Alsace at the time (1800's) had a heavy influence of german culture and people from the region even spoke a dialect of german and alot were even ethnic German. I also have a surname with German origins .Sooo when people ask me what my ancestry is...do i say German or French?