Interesting question. I would say that the average French person would defend the rights of the worker to take strike action without any doubt. When it is a government employer then it becomes even more acceptable. However creating a bit of chaos for a day or two doesn't raise many eyelids, but if it is long running people seem to say, you have made your point, enough is enough. Private company disputes are not very common at all because there are quite extensive dispute resolution processes in place which seem to work quite well.
The problems on the railway are due to different contracts for new employees to those that give amazing perks to existing workers. From what I see people have given up with this group because the offer seems fair. It does not try to take away rights that people have. You can try to say that transport problems here are unique, but you only have to look at the dispute about guards on trains in the UK to see that a long running dispute can make life difficult for people everyday of the week as they struggle to get to work. Looking up at the skies today there are not many less vapour trails than normal.
The role of the press is also different. Far more factual giving a real in depth insight to a dispute, rather than the silly headlines that have become the normal from certain papers. Such disputes will also be discussed at length on TV in a factual way.
Figures suggest that France does have more strikes than the UK, but seeing as they produce as much in four days as the UK does in five even with the strikes, perhaps they can afford it slightly more.