My father has just passed away. He had very little wealth. Am I required to have an act of notoriety to unlock my bank assets?

Everything will depend on the total amount of the deceased's financial assets.
To be able to obtain the payment of the funds, you must provide the bank with an affidavit drawn up by a notary if the amount is greater than 5000 euros.
On the other hand, if the amount is less than 5000 euros, a written certificate signed by all the heirs will suffice (article L312-1-4 of the Monetary and Financial Code). A number of documents must be attached (https://www.service-public.fr/particuliers/vosdroits/F12697).