OK, so the "no public restrooms" has been covered. Things are changing, though: you can use the restrooms at the "mairie" and other public buildings (public libraries, préfecture, etc.). And in touristic places, there definitely are public restrooms available. Maybe not the cleanest places in the world, but, still...

Other cultural differences

• expect everything to be tinier: flats and houses are typically (much) smaller than in the US; cars too, even though big 4x4 and Dodge vans are the latest fad (problem is streets and parking spaces were designed for 2cv).
• food and eating habits: your typical day will include 3 to 4 meals, tops. That would be breakfast (petit déjeuner: typically continental), lunch around noon (might or might not be 3-course meal, again things are changing), "goûter" around 4 pm (especially for kids) and then dinner around 7, but could also be later depending on the family. But never before 6 pm. That would be "goûter" and spoiling your appetite. No snacking. If you're an adult, and it's friday or saturday, you might expect "apéritif" around 7 pm: basically munchies and some wine or beer, before the real thing.
• dog poop. Yes, it has been mentioned elsewhere, but I think this really a cultural exception. I don't know if it's because French people are really anarchists in their hearts, even though we LOVE rules, but if you mention to some dog owner that s/he really should scrape all that nastiness because leaving it on the sidewalks and public parks is not healthy, and kids will definitely step into it etc., well you're asking for trouble. You might even get in a fight! At some point, in the streets of Paris, we had teams of very specialized poop-cleaners. They were equipped with specially designed motorcycles, which included something that looked right out of a Batman or a James Bond movie: a very complicated poop collector, complete with a canister of liquid nitrogen (can you dig this?), and some sort of huge vacuum cleaner. The process would go like this: the "motocrotte" (that was the official name) operator would freeze the poop with liquid nitrogen, then slurp it into some container and move on to the next target. I never got to knew what they did with all the frozen poop at the end of the day, and I don't really want to know. So, yeah, I guess poop collectors are the epitome of French culture: instead of handing fines for getting the streets dirty, you come up with some crazy mechanical contraption from the space industry! And when you think of it, many aspects of life in France are like this: instead of down-to-earth pragmatic solutions to everyday problems, you get a very sophisticated process that only the French can understand.
• administration: I will only say this. Check the 1980's movie "Les 12 travaux d'Astérix". Among the challenges Astérix and Obélix have to face, they must go to an administration ("la maison qui rend fou" the place that makes you go crazy) in order to get some kind of certificate. But to get that, they need yet another certificate, etc. It's almost not a caricature, even in today's administration. To make things worse, in real administrations, you can always expect your application to get lost at some point, so that you have to do it all over again. And then you think back of "la maison qui rend fou"... and wish you had some of that "magical potion" to help you out.

• education system: everything is more or less free in France. University tuitions are around 250 euros a year for years 1 to 3, it gets more expensive for master's degree and PhD (still less than 1000 euros a year). So everything should be fine and we should have the most brilliant Nobel prizes, inventors, have zero unemployment rates and so on. The catch is that the whole education system is really geared towards high profiles. So it's not so much an education system but more of a selection system. If you're already a math head, then congratulations, you'll follow the "voie royale": a curriculum in sciences, an engineer position and you'll make plenty of money. If you have a literary profile with excelent memory, spelling, and dig the whole "lettres classiques/lettres modernes" thing, then congratulations, you'll probably go thrhoug the elitist "hypokhagne, khagne" and "agrégation" circuit, to end up as French teacher in a poor neighborhood college, or maybe if you're smart, as an assistant professor at some university. But if you actually expect to be taught stuff so that you can find a decent job, then you're in for some disappointment. As has been mentioned elsewhere, this is a very deep-rooted French cultural trait: people expect excellency, not just okay-ish capability. As a consequence, it's hard to find typical French people engaging in spontaneous activities (while sober I mean): dancing, singing, acting...
• everything is centralized: France is definitely NOT a federal state. Even though things have supposed to have changed in that respect, everything is still pretty much controlled by Paris. Just have a look at France's highways or railways: everything converges neatly towards Paris.
• religion/politics separation. France is officially a non-religious Republic. So no religious anything (crosses, stars, etc.) in public places or offices. No "So help me God" in public speeches from the President in office. You're NOT supposed to take a day off for religious holidays. You're expected to come to work on fridays, even if it's a prayer day or whatever (ramadan, pasover, you name it). Still, Christmas is all over the place... and almost all public holidays and school vacation periods derive from Christian holidays (Christmas, all saints, Easter...), go figure.