I write a fanfic and the corporation owning the franchise's copyrights never answers to any communication attempt. Can I inform them in writing that, based on the silent consent principle, I consider myself authorized unless they tell me otherwise?

No, you cannot.

Fanfic is copyright violation. Consider yourself lucky that they are ignoring you. If you get too snarky about this and send them a letter, they will notice you, and the notice might well include a letter from a lawyer telling you to cease and desist.