This thread seems to be more of an IMO than a GD, but anyway :
I don’t know if it counts as “values”, but here are some things that seem typically american to me :
- Patriotism (I won’t elaborate about that), and besides that identifying with one’s country. It’s quite noticeable that americans tend to use “we” when refering to past or current events the USA was or is involved in : “we” fought in WWI, “we” tortured Irakis… instead of “The USA fought in WWI”, “American soldiers tortured Irakis”. “We” used in this way isn’t unheard of elsewhere, but it’s not nearly as common. Similarily, a tendancy to feel they’re somehow responsible for the actions of both their government and other americans. For instance american people frequently feel ashamed by the behavior of fellow americans or of their admnistration or apologize on behalf of them. Which is quite contradictory with the following :
-Individualism and confidence in one’s ability to control one’s destiny. As a result, an individual successes and failures tend to be attributed solely to the merits (or lack thereof) of said individual. It seems to me that the traditionnal distrust for the government has something to do with this (Let me alone. The less you will mess up with my life, the better). It seems to me that american people want their turf to be very clearly delimited and separated from other people’s turf and the government’s turf. By the law. Which leads me to :
-Fascination with law and everything legal. I’m not refering only to the “lawsuit culture” but to endless discussions about legal matters, the incredible (negative) attention lawyers receive, the very common depiction of trials in american movies or series (try to find a court scene in a french movie), the overwhelming importance given to the law over, say, common sense, opinion, etc… and even more importantly to the constitution :
-Quasi-religious respect for the constitution. That has been the topic of one of my first thread here. The constitution seems to be viewed as the holy scripture and the founding fathers as the apostoles. Which results for instance in debates about a very contemporary and concrete issue devolving on a regular basis in an argument about what some dude who died two centuries ago had in mind when he wrote a couple lines about a now defunct militia or about whether or not another long dead dude was a christian or a deist. Speaking about the constitution :
-The importance granted to “free speech” to the exclusion of any other consideration. I don’t think I need to elaborate about this. So ingrained that eventually you find americans clamoring about their right to free speech on a foreign ,privately owned, fucking message board.
Some other things :
- A still existing belief in the “manifest destiny”, to some extent. The idea that the USA carries universal values, is somehow special, a beacon of light in the darkness, has reached a perfect form that won’t ever change (see my paragraph about the constitution) despite unending, blatantly obvious cultural and societal changes, the assumption that something american is better by definition (even when the person doesn’t have the slighest clue about how things work elsewhere hence can’t make a comparison) or even the belief that the USA has a peculiar importance in God’s plans, for believers.
-And of course, americans are strongly religious by comparison with other western countries’ citizens. With some amusing peculiarities : people switching denominations on a whim, “shopping around” for a church that gives a better bang for the buck, or viewing their church as a sort of “club” that Jesus probably created so that people could socialize. Excluding fundamentalists, religion viewed as a casual part of life, and for instance people enquiring about a perfect stranger’s religious beliefs in the same way they would ask about their prefered sport.
-The strong belief in the wonders of the free market. The default position that it’s the best solution to any problem until proven otherwise by very compelling evidence.
There are probably more I can’t think of right now.
As for the french values, I couldn’t tell. They would be the “default” values for me, and though I could probably tell whether something in particular is actually “french” if asked , it would probably come with a lot of “but” because I notice more easily the differences of perception within french society that what makes it different from other societies.
Though I would mention we are the only ones apart from the chinese to understand what food and cuisine is really about 
On second thought, I think that “equality” is certainly a central french value. Not only equality before law, but social equality. If you get a larger share of the pie, it must be because you used devious tricks, and you should share with your little brother. There’s some shame attached to being richer, and though it’s significantly less true than it used it be, when an american would be likely to lie to exagerate his income or wealth, a frenchman would tend to lie to underestimate them. I’ve witnessed a large number of “I make less money than you do” piss contests over the years. When income is even mentionned, that is, since it’s not a polite thing to do.
On a related note, I’ve noticed that people from seemingly every country are convinced they are especially prone to complaining, undisciplined, unsatisfied and grumpy.