Has anyone ever stayed in a Bed and Breakfast in Paris?

They are fine. Not sure what you are asking. B&Bs in Paris are the same as elsewhere. And there are a lot of fine little hotels that function like B&Bs.

I've been looking at other types of stay in Paris and thought it might be good to ask about Bed and Breakfasts. It's really just a general question-does it increase the level of formality to stay with others, etc.

I'm not sure what you are asking, either. Do you want to be formal? Less formal? Anyway, Bed and Breakfast establishments are rather the exception in Paris. Many/most hotels have a breakfast room, and you can choose to have breakfast there. Usually you pay extra, and the breakfast usually consists of just a croissant, rolls, coffee -- a "continental" breakfast. We always prefer to eat in some local place rather than in the hotel, as it is more pleasant, and usually costs less. If you are looking for informality, and/or more contact with the host, you might consider AirBnB, http://www.airbnb.com/ which is a site through which people rent rooms in their homes, or apartments, sometimes including breakfast.

Thank you.

Most Paris hotels will also serve soft boiled eggs if you ask.

We just came back from a trip to Paris, Amboise and Normandy. We were in a hotel in Paris but a Bed and Breakfast in Amboise and Bayeux, Normandy. Our experience was that they were wonderful, clean, terrific hosts and delicious breakfast. Wouldn't hesitate to stay in one again.