In this context, "affairs" means "businesses". The phrase "main drag" means the main road through town, usually the main road downtown with a lot of businesses.

A 'drag' is a slang term for a road or street. It is a somewhat stylized way of saying road. It sounds more interesting than the ordinary words 'road' or 'street' that we hear in daily conversation. Describing a restaurant as a 'French affair' is also a stylized way of writing. It literally just means 'French restaurant', but the writer may have chosen this phrase to make the passage sound better. I feel that the nuance here is the restaurant will not only be serving French food, but offer an authentic French dining experience.