According to E. D Hirsch in Why Knowledge Matters, the decline in French academic results is attributable to them adopting the individualistic USA model.
Where are you getting the information that the supposedly poor results are because schooling is publicly funded?
And while your examples are also true, I would argue that it's actually normal for rail and post to be in the red. This is because their primary purpose is not to generate revenue for the state, but to provide a service to taxpayers. For example, unprofitable train routes have to be kept because they link remote areas to cities.
In fact, when private industry handles these type of public services, users tend to have poorer service and higher costs, because there is a natural monopoly.
For train service, take a look at the UK, where different companies "compete": service is worse than France at a higher cost.
La Poste has been a publicly traded company for about 10 years if memory serves. Service has been getting worse ever since.
That's how you end up with "Education" being the first cost element of the French budget (about 72 billions EUR per year) despite pretty poor academic results (that can be easily observed in the ever-decreasing level of the national exams). When government manages everything in one field, that field becomes mismanaged (trains: SNCF always in the red, the post office: ever increasing costs for users year after year, etc...)