As you probably know, California does not tax Paid Family Leave (PFL) Benefits.
PFL that is taxable on the federal return is excludable if it is paid by either the state's Employment Development Department (EDD) and appears on a 1099-G form, or is paid by an insurance company under a Voluntary Plan for Disability Insurance (VPDI) and reported on a W-2. It is not included in your employer's regular W-2 but on a separate W-2 from the insurer.
It sounds like your PFL was included on your regular W-2 from your employer, not on a 1099-G or a separate W-2 from an insurer. It is both taxable federally and to the State of California.
As the TurboTax onscreen instructions point out, "Don't include PFL income that was paid directly by your employer. This type of income is normal taxable wages." Any amount reported by your employer in box 16 of a W-2 is considered by CA as compensation for services or taxable fringe benefits.
It may be that you received short-term disability pay rather than officially PFL under a Voluntary Plan for Disability Insurance (VPDI). Generally, excludable PFL kicks in after all of your employer-paid benefits (vacation, sick leave, short-term disability) have been exhausted.
California employers seem to use the term "paid family leave" loosely which causes taxpayers confusion when they discover when "PFL" is taxable and when it is not.
You may be able to appeal CA's penalty under the "first-time penalty abatement" law passed by CA in 2014. While this regulation (Section 19132.5) isn't easily spotted on the Franchise Tax Board's website, it requires the FTB upon request of a taxpayer to abate a failure-to-pay timeliness penalty when the taxpayer has paid all tax currently due and has not had a similar penalty in the prior 4 years. File a Form FTB 2917, Reasonable Cause -Individual and Fiduciary Claim for Refund, available at https://www.ftb.ca.gov/forms/misc/2917.pdf
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