Well, Wikipedia has a pretty detailed explanation on this:
Alsace-Moselle maintains its own local legislation, applying specific customs and laws on certain issues in spite of its being an integral part of France. These laws are principally in areas that France addressed by changing its own law in the period 1871–1919, when Alsace-Moselle was a part of Germany. [...]
Perhaps the most striking of the legal differences between interior France and Alsace-Moselle is the absence in Alsace-Moselle of a separation of church and state (cf. 1905 French law on the Separation of the Churches and the State), even though a constitutional right of freedom of religion is guaranteed by the French government. Alsace-Moselle is still governed by a pre-1905 French law established by the Concordat of 1801 which provides for the public subsidy to the Roman Catholic Dioceses of Metz and of Strasbourg, the Lutheran Protestant Church of Augsburg Confession of Alsace and Lorraine, the Calvinist Protestant Reformed Church of Alsace and Lorraine and the Jewish religion of the three local Israelite consistorial ambits of Colmar, Metz, and Strasbourg, as well as providing for public education in these faiths; although parents are allowed to refuse religious education for their children. The clergy for these religions are on the state's payroll. Catholic bishops are named by the President of the French Republic following a proposal by the Pope. The heads of the Lutheran and Calvinist churches are appointed by the prime minister, after being elected by the competent religious bodies. The public University of Strasbourg has courses in theology and is famous for its teaching of Protestant theology.
The same article notes that the decision to continue to apply this local law was taken in France (as opposed to, say, a treaty) in 1919 and extended a few times, most recently (and indefinitely) in 1951. It doesn't get into the rationale(s) for the French post-WWI decision(s) much, but I'm guessing it was in the interest of "not rocking the boat" in a sensitive border region.