What age are your children?
The feedback that I hear is...
ISL - to only truly international option. Teaching in English, working towards IB / IGCSEs. Very high fees (often paid by employer). Attracts a lot of US expats who don't need/want to integrate into France but want their kids to be able to slot into Int school wherever they land next. Not bilingual in the slightest - kids can go through ISL from kindergarten to IB and still only speak rudimentary French.
CSI - French state school so crappy building and not great facilities, majority of teaching in French (6 hrs a week English in primary, then specific subjects at college / lycée). Yr children (depending on age) will be offered French lessons to help them adjust but they will be expected to become properly bilingual in French and English in order to progress. Very 'French' on the French side - highly academic, old-fashioned chalk-n-talk teaching, heavy focus on maths / French / science. Students work towards the OIB which is a French Bac with specific subjects taught in English. Reputation for very good results, academically. Anglophone section is fee-paying, but not private school fee levels. Very difficult to get in, at all levels due to limited places and huge demand.
Ombrosa - for French parents who want their children to speak English, and British / Americans who want the private school experience - nice buildings, landscaped grounds etc. Still pretty French in terms teaching, I've got friends who love it, others who've taken their kids out sharpish.
There are various other 'bilingual' options, including some private catholic schools which currently claim to offer an anglophone section as per CSI i.e. Some hours a week taught in English. Generally, they are all full of French kids whose parents want them to learn English, they really aren't truly bilingual. None have been accredited to offer the OIB yet and again, they attract French families.
Depending on yr kids ago you could also consider local French schools, especially if you are all English at home? Depends on yr longer term plans I guess.
Bon courage!