The first thing to remember is that only some countries allow dual citizenship. Many other countries only allow it in certain circumstances. In many countries though, if you get naturalised (take citizenship) in that country, you have to give up your old citizenship. In some you have to take an oath that you "forsake all previous allegiances" or something like that but that's usually not held to actually mean anything.Wikipedia tells me that France didn't allow dual citizenship until 2021 (French nationality law). I don't know if this means people who had to give up French citizenship to take up a new citizenship can now get it back or not. America does allow dual citizenship but doesn't encourage it.Some people manage to get away with having two citizenships illegally. Usually this happens when they take up a new citizenship but simply don't tell their old country. I don't know of anybody being charged for this, and at least until your passport expires you'd be unlikely to be charged so you wouldn't even be committing any sort of "lying to the government" type crimes if they exist.(disclaimer: I am so not a lawyer. I'm the least lawerly person around. I'm no expert on any of this stuff).Anyway, if you do have dual citizenship, how it works is you are a citizen of both countries. It doesn't "halve" your citizenship in either country. You have the rights and responsibilities of both countries. Often if you grow up and live in a foreign country you have less responsibilities in your country (the country of your citizenship), such as for example the requirement to do military service (France no longer has compulsory military service and I don't know what the law was for non-resident citizens back when it did, but I'm talking in general).For an American citizen (including a dual national) this would entail the requirement to do a tax return every year, even if you don't live in the country. This is why many Americans chose to give up their American citizenship.But in terms of travelling, the example you gave is exactly how it works. If someone is a dual French-US citizen, they are both a complete citizen of the USA and a complete citizen of France.The USA has a law that if you are a dual citizen (with one citizenship being of the USA) you must enter and exist the USA with your American passport. This is a good idea anyway. So if your friend wants to visit (or live in) the USA, he should enter on his American passport (and, if he leaves, obviously, exit on his American passport).I don't think France has such a rule. If it did, it would be unworkable, since there are no border checks between France and any of its land border crossings, and they couldn't prevent a French national from going to Germany with an American passport and then driving, walking or taking the train, to France.But it's still a good idea to enter on his French passport. If he decides to stay in the Schengen zone longer than the three months that an American can normally stay, or he decides to work, he doesn't have any difficulty staying, and doesn't have people asking questions when he exits.In terms of going to China, or any other country that's not the USA nor in Schengen or the EU, he can use whichever passport he wants. My guess would be that he went to China with his Chinese passport because he applied for the Chinese Visa at the Chinese embassy in the USA?This is perfectly legitimate. Some embassies will get confused though if you're for example in the USA and you try to ask for a visa on your (e.g.) French passport, but there's no American entry stamp on your French passport. It would look like he had entered the USA illegally. So if he was in the USA and wanted to get a Chinese visa, it would be much simpler to request the visa on his American passport.