score:4
You're right that applying to the French consulate is fraught with difficulty and likely not to work. But you could try, if you are completely upfront (don't cheat and lie about your intentions), you don't risk a refusal (which would have all sorts of unpleasant circumstances) but only a rejection (the consulate will promptly decline to process your application and you should get your fee and documents back). If you try this, join a letter explaining why to your application, it might help too.
A few other things you might try is finding another German consulate (if needed in a neighbouring country you can access easily) or keep watching the schedule to see if new appointment slots open.
In any case, three month waiting time is not acceptable (people are not supposed to apply more than three months in advance!) so you can certainly try to contact the German consulate (politely, don't act entitled or angry even if you and I know they are at fault) and ask if they can suggest a solution.
Upvote:0
Just change your travel plan say you will stay 3 nights in Germany. Or say you will stay more nights in France, you will need to book additional nights accommodation but you can cancel the booking after you got your visa. It's really that simple. I have applied schegen visa through french ambassy couple of times without even landing in the country . All you need is a proper travel plan and accommodation booking (cancellable) that proves your plan, and the flight tickets proves the plan, of course that needs to be cancellable (business class). It's nothing but a paperwork game. And most importantl of all, this is all legal , you can change your plan right?