Just remember that things don't happen particularly fast in France - most particularly during the months of July and August.
The best you'll be able to do with the OFII, for example, is to send in your paperwork (whatever you have been given) or to check in with them to let them know you have arrived. Any OFII appointment will be set up by them when they have dates set up and available. If you're arriving in two weeks, I wouldn't expect to hear back from them until September (when France comes back to life after the summer holidays).
Hadn't heard of Lebara for mobile phones before. Fine, if you think they fit your needs, but you may want to consider getting a "local" mobile phone (though chances are, you'll need to establish a bank account here first). I only notice that they charge 0,15€ a minute to fixed phones, which is pretty steep for calls within France. Free, Sosh, Red, BandYou, all offer "free" calls back to the US and a reasonable data package. But it depends on your personal usage.
I haven't had a bank require birth certificates, but has been a while now since I opened a new bank account - and be careful because in many instances, those who do require birth certs will want them to be less than 3 months old. (I.e. the copy stamped and dated within the last 3 months). Naturalization certificate is always useful.
One thing might be to stop by your local mairie, if only to introduce yourselves and ask what, if any registrations (say, for the kids' school) are needed. There aren't all that many things that are handled by the mairies these days, but it always pays to have a "friend" at the mairie who knows that you're new in town and trying to do the right thing.