In order to prevent the return of the Victorian mill houses, it is a vital right to be able to withdraw your labour.
Yup. Resign.
Stop thinking in the past. There is a big competitive job market out there. If you don't like the conditions in the job that you're in, go and get another job. If you can't find one that is better, then you're in the best job that's available to you, so grin and bear it!
Best for French ATC would be for it to be split up into different regions as entirely different employers and the employees to get a share out of the money made from the traffic 'carried'. With that if one region decided to go on strike (e.g. Bordeaux), everyone could route through the other regions (e.g. Marseille) instead and the ATCs there could earn more out of the folly of their colleagues in the striking sector!