Hi again, dinner salvaged but then glass of wine and bed...
The above are great suggestions.
I'm thinking quite possibly your lab will love this move, and depending on how much he/she needs to run, you may find yourself leaning towards the suburbs that have been mentioned, all the lures of central Paris notwithstanding!!!
I don't know when your dd turns 3, but in some schools you can get nursery places from 2.5 yrs. If you decide to live in Le Vésinet you could choose between:
Stepping Stones Nursery (Vesinet)
Pre-Elementary Bilingual School (Boulogne-Billancourt)
Ecole Internationale Malherbe (Vesinet)
If you decide on Boulogne-Billancourt to live, then you could add Marymount (US flavour) in Neuilly to your list of accessible schools (though whether it's accessible financially is another matter very high fees and a whopping one-off "capital assessment charge" at enrolment. Also note that you might be crossing the notorious Bois de Boulogne to get there, giving rise to the need to explain about/artfully ignore those nice ladies not all of them actually ladies -- in short skirts waiting on the lay-bys).
And of course BSP everyone loves, but it is also very expensive. Has uniforms too, which not many people are used to any more! But really, parents love this school, and those that have kids in three or four different places really appreciate how it goes "over and above", as compared to almost any other school.
Since I haven't rented in many years, I had a quick look on local estate agents sites and I take back what I said above, it does look like you can get very decent houses with small gardens, two or three beds two baths for around the 3,500 region... and very roomy, comfortable and stylish houses (eg 5 beds 2 baths) are in the 4,500 and up region.
MESSAGE is a brilliant place to join and you can get more first-hand appraisals of the above schools, might be worth doing since all I know is through word of mouth, I'm afraid!
Best of luck.