France pension system isn't close to bankruptcy. It needs some adjustment but pushing retirement age isn't the only option. Also one thing to understand is that there are two criteria to get a full pension
1. work 43 years (this used to be 36.5 but has been increased 10 years ago), so we're not feeling this yet
2. be at least 62
The reform wants to push 62 to 64 in 2. The problem is that educated people will already retire after 64 because of the first constraint. So this reform targets explicitly those who started to work younger, and who are also those with lower life expectancy and with the hardest job. This is unfair. At the same time, France (as in French citizen) has never been as rich in history as it is now. There should be better wealth redistribution here. It's very apparent when you look at the numbers.
Another issue is employment. In practice, a lot of people struggle to find a job when they are 55+. These reforms will increase poverty in the country.
Last point. France isn't like the US were people are incentized to build equity for their retirement. The rule of the game here is that current employees pay for retirees and in exchange expect their pension to be taken care of when they are older. The rules are changing midway and people are upset about it.