I'd be sending the French Embassy an email now (in French, if you can).
Must the visa be processed in your country of origin?
The official stance may be no but if you ask and explain your circumstances, sometimes there's room for movement.
I'd ask at a few French embassies in neighbouring Asian countries if they'll do it.
It may be expensive and time-consuming to return to the US to get your French visa done.
If it's possible, it would be cheaper and faster to get it done in a neighbouring Asian country than for you to fly back to the US.
Singapore, Malaysia, Japan and the Phillipines should be visa-free for US passport holders.
China, Cambodia and Vietman may require visas for entry - and the cost of the visa varies but can be US$100+.
Apart from doing the visa in HK itself, the French embassy in Beijing/Shanghai (or even Shenzen or Guangdong?) may be your most economical option. Flights and trains from HK should be inexpensive and plentiful.
But it's all contingent on who says yes.