I don't know exactly how it works, but if the U.S. does recognize your French citizenship, well then, sorry--no security clearance for you.
That's a meaningless statement. I can't imagine any reason for the US to need to recognize the dual citizenship status of one of its own citizens.
You can't use the fact of having a foreign citizenship as a defense for braking any American laws. Or to seek a special (American) status.
Which is again my point. "Dual citizenship" is a paper issue and nothing else.
If you're reading this Ashley: I put "dual citizenship" in quotation marks for you.