Dvushka, can I ask what your, and your DH's native languages are? (Sorry if I missed that somewhere in the thread)
So, your main aim is for your DC to learn French. Right. I have seen children of 4/5/6/7 move to Paris, and it's taken them at least a year to settle into school and feel confident amongst their piers. I've also seen Polish children come to England and would say it also takes them a year to settle a converse happily with other English children)
However, after a year they still don't have the full vocab a native child would have, and this can, at times be unsettling for them.
Can I also ask why Paris? It it partly because you want to live there (I can totally understand that!) Personally I would be keener to move to deep dark France, if it's solely for language reasons, as there will be far fewer English Speakers.I suspect you may end up socialising with the other parents at EAB in English, as will your DC.
I don't think anyone is name calling going on here, I just think people think you are are slightly misguided as to how much immersion a child needs to become fluent.
At the end of the day, from what I have witnessed, it is the language which is spoken at home in which children are the most articulate/comfortable.Of course that can easily be two languages, with the language of the country in which they live being the third.