As an unvaxxed adult traveling to France, the French system requires me to have a "compelling reason to travel" which is set out on a permit form....Looking through the list of "compelling reasons" listed in the permit here there's nothing resembling "humanitarian reasons". That may be because it would sound too general but we have to remember that even in the UK people were prevented by the animals in charge from, for example, saying goodbye to dying relatives. I don't think the French authorities can be expected to be "kinder & gentler" during the Covid panic. I'd be inclined to give the French Consulate in London a ring and decide on your next steps based on the tenor of their response. It's only one phone call.
If you enter France in transit you have 24 hours to leave. If you don't leave they WILL know. When you do eventually leave I imagine border control will point out that you committed a crime & present you with a huge fine.
I drove down and said I was a delivery driver, seemed to satisfy them.
