Since you will soon be leaving for the UK, and you will return not return until autumn, who takes care of the pool while you are away?
I can't say that leaving the pool as is and letting the algae continue will cause irreparable damage, one thing that can happen is that once all the chlorine is depleted, a bacteria can consume the CYA and the breakdown of CYA creates ammonia, and to clear the ammonia requires 10ppm of chlorine to oxidize 1ppm of ammonia.
There is a method of reducing CYA without draining, but I don't know if it's available in France. I live in the eastern US and I have never heard of it being used here (water is too cheap), but in the western US, they use reverse osmosis. Reverse Osmosis processes your water, removing dissolved solids like CYA and calcium. This could be great benefit for you. The process is done by specialized contractors in the US.
If you can't get Reverse Osmosis and you are running out of time,,,,,this goes against a lot of what this site tries to teach, you are in a situation where you do not have the time to correct your pool chemistry. You might want to consider hiring a pool maintenance company, they probably won't follow the TFP methods, and they will likely dump chemicals in we don't use, but maybe, just maybe they can fix your problem.