Hello and welcome to Wefugees!
I'm afraid that we can't judge from afar whether or when the so-called ‘transfer deadline’ will expire. Normally, the transfer period runs for 6 months from the date of approval by the responsible EU member state (in your case France). In some cases, however, the deadline is extended (12-18 months). Especially if the authorities assume that the person concerned has absconded (in practice, this extension happens again and again, although the asylum seeker has not absconded at all). Did the BAMF's negative decision really only come in May 2025 or already in 2024? Actually, the BAMF also states when the deadline expires - but I think that this is often difficult to filter out from the documents. I would strongly recommend that you ask a counselling centre for support (the asylum procedure counselling centre would be the best place to go - the "Asylverfahrensberatung"/AVB). The counsellors can also ask the BAMF about the deadline so that you get reliable information in the end. You may use this search engine to find contact details of counselling services in your area.
I hope this helps and please don't hesitate to get back to us with any further questions.
All the best,
Meike