Welcome to the Wefugees Community and thank you for reaching out to us.
Your situation seems to be complicated indeed and I am afraid that there are no simple answers to your question.
In general, it is regulated in the German law that people arriving in Germany (and want to apply for asylum) need to express the asylum claim at the authorities (i.e. police or refugee reception centre) immediately (as far as I know, within one week) - otherwise, the chances to get accepted as refugee in Germany will decrease significantly (if there are no credible reasons for the delay).
In your case, I see another issue: According to the so-called Dublin regulation (EU law), the country which initially issued the visa is responsible for a potential asylum procedure of the visa holder in the first place. My dear colleague Alla explained this process here as well. Therefore, the German authorities most probably will try to send you back to France.
I read in your other thread that you are arriving in Berlin. I would highly recommend you to contact a migration/refugee counselling office there. One option will be the asylum procedure counselling of the organisation "AWO" (Asylverfahrensberatung) - they are specialized on the asylum regulations (incl. the Dublin procedure). Please follow the link for the contact details. Don't hesitate to call them - I am sure they speak English as well!
In any case, please also don't hesitate to get back to us with any further questions.
All the best,