Notorisation of the document means signing the document in front of the Notary. It assures the parties of a transaction that a document is authentic.
Franking is the procedure to stamp duty, you may either buy stamp papers of that particular value or get it franked. (You might have done the same for your CA Articleship registration)
A partnership firm can be formed even based on an oral agreement. However, in order to avoid any unpleasant situations in the future, it is advisable to ensure that the agreement is in written form. And for the purpose of the registration of the partnership firm, you need to get your partnership agreement notarised and also franking/stamp duty is necessary.