Thank you for contributing to our community with your question and Welcome :-)
I had a look and found these really helpful websites stating what you have to do if you want to seek asylum in France. The first one is a French refugee support and information website that includes a very long explanation of the asylum procedure:
The infomigrants website here also lists the steps you need to take:
And here is a website (Asylum in Europe) describing the regular asylum procedure in France:
Of course other members can share their experiences here as well!
I hope these sources help. Feel free to reach out to us again if you need any further assistance or if anything is still unclear!
All the best,