Do I have to appoint an agent? What is his/her role?

It is not mandatory to appoint an agent. However, to ensure a smooth relationship with the French authorities, you could always appoint an agent who will carry out the procedures on your behalf and under your responsibility. He/she will be the intermediary between the authorities and your foreign company.

In this case, you should execute a power of attorney and send the original to the Foreign Business Tax Department.

A template for appointing an agent is available in the Bulletin Officiel des Finances Publiques: BOI-LETTRE-000215-20130417.