(a) For US tax purposes you are taxed as if you are ONLY a US citizen
(b) You are taxed by US on your world income but may be eligible for foreign tax credit/deduction on income that is taxed by both jurisdictions ( US and France )
(c) From your post it appears you are a resident ( & citizen of France ) and therefore taxed on world income ( same as US ),
(d) For form 8938 ( FATCA) form, other than ticking the boxes schedule- B as to whether you have to file FBAR ( form 114 at FinCen.gov and only on-line filing, threshold of => US$10,000) and filing the form 8938 ( FATCA with a threshold depending on your filing status -- MFJ/MFS/Single etc. and tax home) there is no other requirement and NO TAX consequences.
(e) Noting that US taxes you one your world income , the US$10,000 + effect is really based on whether this was income ( active or passive ) that needs to be taxed or not . Just telling IRS that you have an amount in your bank account does not necessarily mean more taxes.
(f) Since your tax home is foreign ( FRANCE), your income(s) may be eligible for foreign earned income exclusion and / or foreign tax credit. There fore I am not sure I understand the import of the question you posed.
If I have not addressed your "real" question, please consider adding more explanation to your post.
Is there more I can do for you ? Is this for tax year 2022 or for 2023 ?
pk