Can I skip the FBAR if my foreign bank is already reporting my account to the IRS under FATCA?

No. The fact that your foreign bank reports your account to the IRS under FATCA does not relieve you of your own FBAR obligation. They are parallel systems: FATCA imposes reporting on the financial institution and, separately, on you through Form 8938, while the FBAR is your own filing to FinCEN. The IRS actually cross-checks bank-reported FATCA data against the FBARs and returns individuals file, so relying on the bank to cover you is exactly how discrepancies get flagged. If your aggregate foreign balances exceed $10,000 at any point in the year, you must file the FBAR yourself regardless of what your bank does. Treat your personal filings as mandatory and independent. The bank reporting your account is a reason to be more careful, not less.