What is true is that SNCF▸ are pursuing their programme of level crossing closure much more actively than NR» (quelle surprise!). The next two crossing from PN16 at St Gilles were closed about five years ago, and replaced by a bridge, though the traffic (even in the holiday season) hardly makes that vital. Note that there are still barriers, even for the bridge...
Is that all down to NR or is it that SNCF don't have to pander to local NIMBYs.
Hard to say, really, partly due to the lack of good data, but I think it has more to do with the integrated nature of French government (including SNCF). The NIMBYs, and they do exist, are likely to be well represented inside government, especially at the lowest (commune) level which is responsible for minor roads.
It's not the size of the budget - SNCF R^seau refer to ^35 or 50M a year, and say a closure (not clearly defined) costs ^3-10M. SNCF only contributes part of the cost, so I suspect the various levels of government may be putting in more than here. Note also that ^10M upper cost figure - that should apply to a bridge over or under a major road. If it does, that bears out the suggestion that such civil engineering jobs cost a lot more here than elsewhere in Europe (and France in particular).
Government does more direct supervision of SNCF and other actors, rather than pretending they are independent and negotiating contracts with them. That's partly a different mindset, and partly that SNCF has always been a part of government, and has never had its legal status changed by privatisation or "privatisation". Of course being nore integrated with government doesn't necessarily help.
In terms of administrative efficiency or complexity, the French model is famous for being slow and cumbersome, with lots of overlapping responsibilities. For level crossing there is a coordinating body, created in 1997, headed by the ministry (of ecology, sustainable development, and energy - which now includes transport). Two directorates of this ministry supervise SNCF: transport infrastructure (for SNCF R^seau) and transport services (for SNCF Mobilit^s). This coordinating group for the improvement of safety at level crossings includes representation from SNCF, regions, other local government, research bodies, etc. And during the last year, at least two more committees have been created by the transport minister to do with railway safety in general or level crossings.
But once it decides to do something, it can be very effective. Think about roundabouts or cycle paths, both of which were rare in France not long ago (about 25 years and 15 years respectively). Then they were identified centrally as "good things", and slowly started to appear all over the country. Now both are more common than they are here - there's a kind of momentum that keeps the process going. But having said that, any one level crossing closure can still take many years.
I can think of two specific features of the French system that may contribute. On is the prefect and prefecture, meaning that a significant part of central government is split into 100 local parts, headed by a kind of generalised deputy minister. That allows central government to coordinate local government in a very detailed way. The second is that consultations and enquiries seem to be less independent - being run by the central government departments or agencies. So yes, there is local consultation, but it's less of an adversarial either/or decision, more of an enquiry to find the "best" solution.