Visa appointment date may be up to six months before the visa start date
If you find yourself in the unfortunate position of a potential or actual overstay of your Schengen 90 days or Visa End Date due to a genuine emergency then your first point of call will be the local prefecture who have the authority to deal with such events. You may wish to also consider contacting your Maire or the British Consulate/Embassy.
For a visa the exit requirement is to leave France by the end of the visa period; whereas at the end of your Schengen 90 days you must leave the Schengen Area.
Be aware that should your planned mode of transport be no longer possible then you may be expected to use another one. For instance:
if you are unable to fly then you might be expected to use a train unless there were medical grounds for not doing so; or
your car breaks down but your breakdown cover provides you with an alternative method of returning home.
In a medical emergency you should gather evidence of hospitalisation, prognosis, and any advice offered by the medical professionals concerning onward travel and present this to the prefecture. The process may take a few dates before a decision is taken.