It doesn't need to separate train operations from rail track network maintenance. It doesn't need to open up the network to competition.
What it needs to do is cut the number of excessive public sector workers, reduce costs, and stop running the business like a political arm of the government.
I can bet that the reason they think they need to do all these things is that cost pressure is rising on them, and they think they need to branch out / cut off compartments of the business to make it better. But this is tinkering rather than addressing the fundamental issues (inability to fire people, change cost structure, etc. due to political interference).
Public rail is a money-losing venture, in every country (except Hong Kong). That's what "public" means. But it's important to have. Just how much money-losing depends on the political environment and skill of the management. UK tried this sort of thing and it left everyone with a shittier experience, though they could claim that they successfully privatized the industry -- everyone knows that's a total lie.
At least France has a history of pride in the speed of the trains, so that will keep things in check a bit. They'll pay through the nose for it though.