I lived in Paris for 6 years between the ages of 12 and 18 and went to the British School. It's a fantastic school and I loved it there. It's small size meant that I built a really good relationship with the teachers. It's very multicultural and I made friends from all over the world. There were fantastic sporting oppotunities, the hockey and rugby teams travelled all over europe to play other international schools. I went to Rome for a week on a theatre workshop. There were also school plays, choir, orchestra etc.
On the other hand, I had friends who went to the International School, and the academic achievement there seemed to be really high, probably higher standards to the BSP, with the additional bonus becoming bilingual.
I would think about whether you want to separate your dd's when you are uprooting to a foreign country, or whether they would be happier going to the same school. It's certainly not too late to send your 11yo to the international school, if you find that the better option.
We lived in the South West in a village called Bailly, about 5 kms from Versaille (me and sister used to cycle to the palace gardens in the summer for picnics). I think the closest train station on the SNCF was Noisy-le-Roi. A lot of my friends lived in and around St Nom la Breteche. The BSP used to organise private coaches to school and these villages were on the bus routes, plus the HM at the time lived in our village which influenced my parents choice of where to live.
I could go on and on. I loved living in Paris, it's a unique and exciting opportunity. And you're close to the UK if you feel homesick.
I lived there 20 years ago, so much will have changed. I'm sure whichever school you choose, they will be happy to give you further advice on choosing places to live etc. My parents went out for a week before we moved there to check out different areas and find a house. Good luck and hope the experience is as positive for your family as it was for me!