If you are interested in French schools I would look at the schools in Paris which follow the bilingual model succesfully: EAB and EABJM.
Personally I feel you would have a selling point if you offered the IB at 6th form - being a bilingual school you have a huge advantage in that most pupils will be able to fly through by language components. The French Lycee doesn't offer it (being bound to the French curriculum) - in addition to the French bac. I don't think you need to offer A-levels, anyone with a desperate yearning to do those will probably just move their child for 6th form.
The French and British curricula have some very fundamental differences. I would definitely advise researching those and deciding whether you want to follow one, both or neither. You may also want to incorporate some elements of the IB programme early on but I personally don't want a school which follows PYP in any language for my children - too much potential to go wrong.
Will your teachers be native French and native English, French trained and British trained respectively? Will you insist your teachers are bilingual? How/where will you recruit them from? What experience of bilingual education will you require?
If you can deliver the holy grail of an French medium English prep you're onto a winner really.
You will need a fair mix of French mother tongue and Enlgish mother tongue children - as NappyValleyMum pointed out French immersion isn't the greatest way to go. You don't get the playground element!
I am assuming you're looking at a French school because you speak French/have some connection with that already?