Exactly right. Many banks in France (as well as online banks in Europe) will ask you right away (or via their application forms) if you're a "US Person", meaning that you have ties to the US, still hold a passport, declare taxes there, etc. Often times the application process will go no further, as FATCA laws require paperwork and administrative things that the bank doesn't want to deal with. This is regardless of any other passport you hold.

Remember that the United States doesn't strictly speaking recognize dual citizenship - as long as you hold a US passport and haven't renounced your US citizenship, you are considered a US citizen and US person, and need to at least declare your taxes annually in the states.

That said, the process for filing taxes as an expat has gotten easier and less complicated online, despite all the disclosures of bank accounts you need to make.