Hi
This region was always a border region between Latinoid speaking regions to the West and Germanoid speaking peoples to the east since Julius Caesar first conquered the area for the Romans c. 54 BC. Previous to that, it was a border region for Celtic tribes and Germanic tribes. After about 405 AD, Germanic tribes flooded the region, and it remained Germanic speaking even after the division in 843 AD of the Frankish Empire into "French" and "Germanic" states.
Starting around 1477, France began to advance eastwards at the expense of the Holy Roman Empire, which is what the Germanic part of the old Frankish empire had evolved into. This trend accelerated especially after the Thirty Year's War (1618-1648) which saw the HRE fragmented into many smaller states. Later, French was taught in the schools of what is now the French province of Lorraine, but I have met a young lady from there who spoke a German dialect. As a border region, the people would have been influenced by both of the neighboring lands, with nearby Luxemburg being an example of a place which has its own language, built with components of both French and German.
The area has changed hands several times during the last couple of hundred years, corresponding to the fortunes of war of Germany and France.
I would think that this is not an easy question to answer. What would influence my thinking would be what language was spoken at home, what their names were (spelling and roots of last names, French or German variants i.e. "Louis" vs. "Ludwig" "Henri" vs. "Heinrich"). One can easily wonder if it really matters at all, and it probably would hang on which army your ancestors joined in the numerous wars fought over the place.
