So the track access charging regime is bad.
Possibly for achieving the type of train service you would like to see, but not necessarily for the needs of France?
Except that in other countries (Britain, Germany, Japan, Taiwan) there is a similar and consistent long distance service all day. This includes the Tokaido Shinkansen with the world’s highest ridership.
This is France we are talking about, which has a different demographic, population density, geography and therefore demand profile than any of the countries you mention. I don't see the relevance in trying to compare the French railway system with any of those countries.
So you are saying the demand between Lyon and Toulouse is lower than on the West Highland line?
I think it would be closer (although not perfect) to be comparing the Marseilles-Gap-Briancon line with the West Highland line. Glasgow is a much larger place than Fort William (for commercial and leisure activities not available in Fort William), and is a major interchange to services further afield. Lyon and Toulouse are of a similar size and would not interact with each other for transport demand in the same way. I would think that the seating capacity of the Lyon-Toulouse trains that do run would be about double that of the current Glasgow-Fort William trains. As far as I know, there is no issue of trains between Lyon and Toulouse being routinely sold out, which would seem to indicate that the current capacity is sufficient for demand?
The other thing that is true is that even if additional peak service into Paris in the morning is desired that doesn’t clash with service for Britain or the Low Countries.
The first train from Amsterdam that leaves at 6am doesn’t get to Paris as it is until 9:30am, and the first train from London leaving at 6am doesn’t arrive until 9:20am.
Realistically any connecting service at Lille with a reasonable time to change wouldn’t be using the Paris Interconnection until basically 10am.
I do not think it is line capacity that is necessarily the issue, it is that the train peak is bringing passengers from the provinces into Paris up to about 11am (bearing in mind the long distances and (for political reasons) the diverse number of destinations), and the peak of return demand from about 4pm onwards. I would think this leaves a lot of trains in Paris with (relatively) short amounts of spare time, which limits the possibility of trips in the middle of the day. Most of their trains are used coping with this peak flow, with a relatively thin service contra flow (which copes with the lesser demand). Couple that with the extra peaks for Friday/Sunday, so the number of trains in for maintenance/servicing are concentrated to the middle of the week, and you can see how they get their uneven timetables. Coping with these peaks and running clock face interval timetables all day is going to use more trains and more staff with uncertain additional revenue to pay for it (assuming the funding is available to them anyway).
Any extra services to Lille (unless they come from Paris) via the Interconnection are most likely to take extra trains and staff.
Analyse their timetables and train diagrams, and analyse their demand profile; it can then seen why the timetables are like they are. Clock face services would mean owning more trains to run services at times of lower demand (with the financial implications that go with that) and/or trying to force passengers who wish to leave Paris at (e.g.) 5pm to leave at 11am instead. The size of France, coupled with the size and economic position of Paris, results in the service which they have. Could it be changed? Yes, but at quite some expense which they presumably do not want to incur.
I don't buy the argument that Paris - Frankfurt/Stuttgart demand is directionally concentrated. Frankfurt and Stuttgart are metropolitan business centres and leisure travel hubs. Each of these two markets should be at least as strong as Paris - Geneva which operates a clockface 2-hourly all-day. The difference I suspect is that DB isn't as proactive and competent as SBB in handholding SNCF. And indeed what with the Rastatt Tunnel collapse, Riedbahn overhaul and the Stuttgart21 saga the infrastructure on the German side has been too unstable to contemplate a systematic timetable redesign. Unlike Switzerland, Germany doesn't have a sufficiently clear takt structure for French trains to plug into.
Paris is much larger than Frankfurt or Stuttgart, and they both lie in Germany compared to France. Neither are really leisure travel hubs [who goes to Frankfurt or Suttgart or their environs for their holiday, or even a 'city break'?] in the same way as Geneva would be to the rest of Switzerland, which is also much closer culturally to France (French speaking part of Switzerland).
As for Toulouse - Lyon, to be fair, the natural demand for medium-sized cities 4 hours apart is going to be limited and there's precious little civilisation between Narbonne and Toulouse, so the basic two-hourly frequency offered by the Bordeaux - Marseille IC services is probably not unreasonable. Again, the problem isn't raw frequency, but the lack of a takt structured around Narbonne (though the Narbonne - Lyon direction frequency is problematic). Clearly 3 trains a day is far too restrictive in terms of times of travel and isn't good enough. For Lyon southwest if you try to just run direct trains to specific directions you will fail as the market isn't thick enough. You need to think in terms of timetabling so that passenger frequencies (through interchanges) are greater than raw train frequencies. It's a matter of how the same set of trains can serve both Lyon - Toulouse and Lyon - Barcelona passengers with consistent journey times and frequencies throughout the day.
Quite.