However there are some problems with this and it's not just the American context that causes trouble, it's also true of France. If any one of you were asked right here, right now, to prove your citizenship, would you be able to do so to the satisfaction of the state in question? I suspect not since most of us don't carry that kind of information on our persons. A driver's license, for example, is not proof of citizenship (my French spouse has an American driver's license and he is not a citizen of the U.S.), neither is a passport or, in some cases, even a national identity card or a birth certificate. To be absolutely100% sure that you are the citizen of the country you claim AND to prove that you are not also the citizen of another country you would need to do some research.
You would have to look at many things pertaining to your ancestors: the birthplaces, marriages, countries of residence or territories and their status at the time of the births, for example. You might even have to know something about the history of the country since territories changed hands rather often in the last century. Then, once you had all that information, you would need to look at the citizenship laws prevailing in the country of residence for say, two or three generations, the laws in force at that time in the home country and then look at whatever the citizenship laws are today. Sound complicated? Indeed it is and I assure you that you might just have a nasty surprise waiting for you at the end of all your hard work. Consider these two cases which I think are excellent examples of the difficulty and complexity involved in proving citizenship.
In 2008 François Werckmeister, born in Switzerland but raised all his life in Alsace (i.e. in France) went to get his French identity card and his passport renewed and was refused. Why? Because Mr. Werckmeister's father was born in Alsace in 1909 when the area was German territory. In order for his father to be considered French he would have had to request a "certificate of re-integration" which he apparently never did and probably never needed to since he seems to have lived out his life quite happily in France. However this caused much headache for his son, who at 56, having never had a doubt that he was French, suddenly found himself not only a foreigner (Swiss/German) but also one who was "sans papiers." This meant no identity card and no passport. He did however at the time the article was written still have his voter registration card so theoretically he could still vote. How ironic is that?
Leeland Davidson, a 95-year old World War II veteran living in Centralia (state of Washington) had a similar tale. Born to American citizens living in British Columbia, Canada, his parents failed to have his birth registered in 1916. That would not really have mattered if Mr. Davidson could have proven that his parents were born in the U.S. Alas for him, his father was born in the state of Iowa several years before that state started issuing official birth certificates. So as far as the U.S. is concerned (and in spite of his military service) he is not an American citizen (he is Canadian) and if he wishes to become an American he must go through the process of naturalization - something that he is quite willing to do though he is understandably quite distressed at the necessity for it.
When I read these stories (and there are others) I came to the rather startling realization that the only people who can be absolutely sure of their citizenship status are naturalized citizens since they are usually the only ones who have had to go through the trouble of proving their former citizenship status in order to acquire a new one. For everyone else, unless he or she can prove otherwise with the appropriate documentation, there must be a doubt.
The good people who are so adamant about requesting identification/proof of citizenship at the polls might want to take this into account. The only way any of us can know our status is to do the research and then have that researched certified by the relevant authorities. This means, at the very least, requesting a "certificate of nationality" (something that exists in both France and the U.S.) from the Federal government.
Since requests for this are relatively rare in the U.S., it is said that acquiring this document can take up to a year. But if people are really serious about making sure that every potential voter showing up at the polls is, in fact, eligible to vote as a bona fide American citizen, then this is what would be required along with a national identity card (one would imagine a biometric card with photo) issued on the basis of that certificate. And it is very clear that, if required to actually prove their status, some Americans who thought they were citizens would be disenfranchised and required to go through the naturalization process before being allowed to vote. A rather sobering thought, isn't it?