When we need anything administrative or official done, we go to the mairie in our village. It's pronounced [may-REE] and it's a feminine word: la mairie. It's where the mayor — le maire — has his or her office. In bigger towns, the same building is often called « l'hôtel de ville » — that's what it's called in Saint-Aignan, for example, and in Paris.
I guess in English it's the village hall, the town hall, or city hall.
I had to go to the mairie a couple of days ago because I got a letter from the tax authorities in Blois asking me whether the work on our house had been finished and whether we had filed a declaration saying as much. We had, actually. I thought the mayor's office, where we filed the papers, would have notified the tax people. I guess they hadn't, but they said they will do so now.
Often the mairie in little towns is in the same building that houses the elementary school. That's the case in our village. You'll see Ecole de Filles — Girls' School — and Ecole de Garçons — Boys' School — engraved in the stone on either end of the building. Nowadays, there's a more modern classroom building located behind the mairie.
You'll also see, in front of the main entrance, a monument dedicated to the memory of those who died in past wars. For such a small (but very old) village, the mairie is quite a grand building.