My mother, a French citizen, passed away in Germany, where she had been living for several years. Which law applies to her estate?

It depends. If your mother has not drawn up a will in which she chooses her national law, the European Inheritance Regulation (n°650/2012 of July 4, 2012) must be applied. This regulation mentions that the applicable law is the of the country in which the deceased resided. Your mother's estate will therefore be settled in accordance with German law.