My understanding at this point is that EABJM will take clever, bilingual children with a good set of reports at age 11; it is a school that is reputed to be very competitive to get into but it is also short, by its own admission, of properly bilingual (French-English) children - it would like these to make up 1/3 of its intake, but it doesn't meet that target. Ergo, if your children are properly bilingual and clever and you live in central Paris and are committed to the school, you stand a very good chance of getting them in.
As new arrivals from the UK (or anywhere else), your chances of getting your children into either EaB or EABJM are higher than those of a local family in mid-cycle as there a certain number of places reserved for new arrivals in France every year.
EaB does (optional) Spanish from age 8 versus EABJM which does Chinese. I prefer Spanish so that is good from my POV, but it wouldn't be a deal breaker as far as I am concerned.
Your DD born in 2001 will be entering CE2 in September 2009 ie she will have three years of primary school ahead of her, of which the first year will be in classe d'adaptation. I think this is plenty of time for a bright child to get acclimatised and learn French well before secondary. Your DS1 will be going into CP (first year of primary) so there shouldn't be much problem for him - he will be more advanced than local children on reading and writing, which will give him some leeway for catching up French and getting used to the more structured environment. DS2 will start petite section in September 2010.
The area around Parc Monceau is great for families - lots of expats (huge numbers of British and Americans, including those married to Frenchmen) and well-to-do French families and lots of fairly casual life in and around the park - an Australian mother commented only this morning when she bumped into me chatting with another school mother on a street corner that "it really is a village around here". I have never lived on the Left Bank - it is very lovely in many ways but I don't feel able to comment about how good it is for families. I think there are more Americans and fewer British families in the 7th.