Beware of the cotisations if you go into the health system... you'll pay about 8-10% of your last year's (worldwide) income if you go into the French healthcare system. Depending on your level of income, that may be fine. Or it may be far cheaper to get private healthcare (check out AARO, for instance).
Also - if you start paying French taxes, you will pay on world-wide income. You'll pay your US taxes, and then pay the French the difference between that and what you would have paid under the French system. PLUS, again depending on your assets, you might be liable for ISF - wealth tax, if you have more than $1.3M (I think) in worldwide assets. Not hard to do if you have real estate and 401ks, which are not excluded from this tax, even though they're essentially pension plans. Francois Hollande intends to ramp that up hard this year. Supposedly it's a one-time deal... but now he's saying it may go on as long as the recession continues.
We were planning to become resident in France this year - we've now decided to stay as US residents, just spending part of the year in France, because of the potential tax burden. We're not particularly wealthy, just comfortable professional class by US standards, but the risk/cost is too great, according to all the advice we're getting. I was ready and willing to pay more tax than in the US, but only to a certain point. (Apart from anything else, I'm expecting a one-time settlement of a lawsuit in the next year or two - if I became resident in France I'd probably have to give 75% of it to the French government. I don't think so.) A dentist chum here on the west coast of France was telling me yesterday that several of his clients - again, not mega-wealthy, just average professional folk - are moving offshore because they're getting so rattled by what this government is doing.
Also - take a look at the capital gains and tax implications of having property/rental property here. Hollande just hiked capital gains - you'd need to keep any property for at least 5 years to avoid punitive tax. Plus once you have tenants in, they have significant rights that can be very problematic for a landlord - it's nothing like renting in the US. I also gather there are new regulations limiting your ability to set rental amounts.
Don't want to discourage you, but just to say you really need to do your homework. Check the US Embassy website - there's a list of accountants and such. You should be able to find someone there to give you advice. It's a real swings and roundabouts deal.