Yes, the California FTB does send out a Letter FTB 3904.
Please see the California Franchise Tax Board's Letters Personal and Business Notices page to verify that the letter you received looks like the sample provided under "Tax Return Filed - Confirmation Required (FTB 3904)," and that the contact phone number matches what's shown on the letter you received.
If the contact number on the letter doesn't match what's shown there in the link, you should contact the number shown in the link to make sure the letter is legitimate.
[Edited 3|17|2020 8:40 am]