Here is a translation of the corresponding explanation on the French Wikipedia site:
T1, T2, T3, etc: T is used for Type, and corresponds to a type of apartment with the number of main rooms indicated. By main room, one means living room, dining room, and bedrooms. Kitchens and bathrooms are not included in the number. Therefore, an apartment with a living room and two bedrooms is a T3.
T1 bis, T2 bis, T3 bis, etc: Those are private lodgings for which one the rooms is large and can be separated in two distinct zones.
F1, F2, F3, etc: F is used for function as in commercial function. Generally, professionals and private individuals uses those apartment the same ways as T apartments.
P1, P2, etc: P corresponds to Pièce which is the French word for Room. This designation is mostly used in the south of France, generally in the same way as T is used.
Studio: Studio is a specific type of F1, where the kitchen is part of the living room/bedroom. In that case, it is an apartment with only one main room with a kitchen corner. Bathroom is separate.
Still according to the Wikipedia article, it is very difficult to find a difference between T and F. No reference texts indicates this information. It seems that progressively, T have replaced F. A few decades ago, T was distinct from F and was more luxurious. T was for more spacious lodgings was F had smaller rooms, like in subsidized housing. In practice, both are used and the F designations tends to disappear in online advertisement.
As far as Chambre de bonne (Maid room) is concerned, another Wikipedia article is providing the following definition: A chambre de bonne is a type of French apartment consisting of a single room in a middle-class house or apartment building. It is generally found on the top floor and only accessible by a staircase; sometimes a separate "service staircase". Initially, these rooms were intended as the bedroom for one of the family's domestics, and the name originates from the colloquial name for such maids: a "bonne à tout faire".