It sounds unlikely that the branch of the French government who is in charge of processing your visa would care to make a determination on behalf of country X about your citizenship there. So in other words I don't think they would care.
Also, unless they are explicitly asking for every one of your nationalities, you are not necessarily obliged to tell all of them to the French visa office. For example I know dual citizens of US and country Y, but when dealing with government of a third country such as France they only write USA in the country of citizenship box.
But I don't really understand why you'd want to use the passport of country X for you visa, in spite of the fact that, if I understand correctly, you're not quite positive you can get that passport renewed. Take a hypothetical situation where that passport expires or gets lost or stolen while you're in France. You next go to the consulate for country X in order to get it reissued. Might the consulate be able to figure your US naturalization and then refuse your passport application? At which point your visa file with the French government might be useless or at least a pain to deal with. I'm only hypothesizing here, and generally I don't like to answer questions this way, but might using the US passport from now on not be more prudent? (In other words, if you already believe that country X would no longer consider you a national were they to know your US naturalization, then why not respect that and act accordingly?)