What does “maîtresse” mean for a dog in French?

When a French story says a dog ran to sa maîtresse, it means its owner. Le maître and la maîtresse are the ordinary words for the person an animal belongs to. Small children use the same word for the woman who teaches them: French primary pupils say la maîtresse, where secondary pupils would say la prof. Context decides which one you are hearing.

The “mistress” sense — a married man’s lover — is real, which is exactly why the context matters, though in day-to-day French the dog and the classroom account for most of the uses you will meet. Le maître d’école is the masculine classroom form, and maître on its own is still the title used in front of a lawyer’s name.