Sorry, this is a long post, but I have been through all these dilemmas and have had experience of a few of the things you ask about!
My son went to L'ecole des Petits in Fulham for 3 years and we live near Southside so it is a bit of a pain as a commute but not too bad. I ended up driving a lot, but it is mostly fine and would take 10-15 minutes, but you would get the odd day when the traffic ground to a halt and it would take 45 mins! I did work very close to the nursery so it wasn't too bad.
The school is really lovely, small and sweet with small class sizes. Don't be put off by the admissions lady, she is a bit of a dragon, but it is in the job description I think... The teachers are all really nice.
Before I went I'd been warned that the parents tended to be very wealthy ladies of leisure with nannies etc, but I found it was a fair mix (the fees prohibit it being a real mix, but some people on limited means who really wanted the bilingual education were making do with grandparent help etc) and everyone is really friendly and its a nice community of both fairly french french and also very international francophones and francophiles. Probably more so than the lycee is now because you have to be so french to get in. The EDP is more similar to what the south ken lycee was when I went to it in the 70s&80s
They do have a very complicated system of options for classes, they have 2 years of english pre-school (half days from 2 1/2 years old, or full days equivalent of english nursery, which follows the english sept-sept year group) and then the fully french classes that follow the french jan-jan age groups and are petite section, moyenne section and grande section. My son did 2 years in the english then grande section. Then got a place at Clancarty Lycee in CP (which was our aim). However, CP in the lycee is a lot more academic than year 1 in the english system, and probably a fair bit more academic than year 2 (it straddles both age groups according to birthday), so my son struggled and it didn't really suit him, and in the end we moved him to an english state school that has a bilingual stream when we got offered a place there. We are now a bit buggered when it comes to secondary schools as we had thought he would go to the lycee in south ken. But we will cross that bridge in a few years...
However, he is doing the private after school french classes at Belleville (french between the commons). So I can advise that these are great, nice small groups and seem to be fun. It is hard as it is 1 1/2 hour twice a week, so they are very tired on the nights they do it, but it means his french reading and writing is still keeping up, although his spoken french is going down hill a bit not having it all day at school. So if you went to Belleville this would be very easy for you, and I believe as a result there are lots of french at Belleville, which is obviously a very desirable school (although I've heard on the grapevine that there is 'a lot of bullying at Belleville', but I don't know how much you want to take the words of 13 year old boys)
From L'ecole des petits in fulham you are guaranteed a place at the lycee, but it could be any of the sites (including ealing! The year above my son, 6 got given ealing - who lived off wandsworth bridge road! but I think by the start of term they had got into fulham or south ken, our year everyone got their first choice i think). If you do the whole primary at ecole de battersea (which is a great school too) then you used to be guaranteed a place in south ken, however now it could be either there or the new Wembley site. But, as the head of Clancarty lycee told me, by the time our children will be looking for secondary schools there might be other options as the population of french in london continues to rise, and there are so many bilingual primary ventures in english state schools, the lycee might well do some secondary school joint ventures to take the pressure off south ken and wembley.
I don't know if that helps you. In the end as people always say, go visit the school, get a feel for whether the philosophy of the education is in line with yours, try to get a feel for what kind of a child you have (hard I know, but are they already very conscientious or very day dreamy then they might continue to be the sort that loves very academic, or the sort that needs to learn through lots of creativity...)
Also, when we were at edp, we did have a few play dates the other side of the cromwell road, or maida vale, but very often you can do play dates in the local park straight after school so it was rare to be going all over the place, and a very large number are walking distance or within 10 mins of the school.
You can PM me if you want to know more!
PS - if you have any preschool children, I'm involved in a lovely playgroup for francophile, it is 'Cadet Rousselle' in Gypsy Hill, I know a bit of a schlep, but there isn't anything like it around, and people come from putney/eltham/surrey to it. Quite low key with nice people involved, meets on a monday morning and is only £3.50 or less per session.