Hi,
I was just talking about this with a colleague of mine and he told me that if you are resident abroad (France, Italy, Germany etc..) and work in Switzerland you should pay the taxes accordingly to the place you are resident (in your case France).
We didn't talk about the case of taxes paied at the source. In this case if your salary is less than 120K gross per year probably nobody will ask you to pay the difference ... even if I don't know if it's legal ... regarding B permit, I wonder how you can have a B permit and be resident in France ... not sure again if it is possible. Maybe just for a transient time before the permit expires ... then you will have the frontaliere permit.
Sorry for not being so helpful but I'm looking for the same info also ;-))