On the cost side, most procedures, drugs and medical acts have regulated tariffs. Doctor's revenues are thus, to a good extent, set by government, and they have lobbied hard to push these higher (drug companies fight hard against the cancellation of reimbursement of not-very-useful drugs, or against the promotion of generic drugs by pharmacists and public campaigns).

Private clinics try to capture a bigger share of the types of interventions which are more profitable (those that don't require long hospitalisations, for instance) and dump the less interesting stuff on public hospitals.

Some of the senior doctors are allowed to spend part of their time at the hospital in their private capacity (where they can charge unlimited amounts of money to patients - and for grave diseases, this is all picked up by Sécu), and they lobby to increase the fraction of time they are allowed to do that.

And of course you have fights over the numerus clausus, ie the number of medical students allowed each year, and the geographical repartition of doctors around France (Big cities and the South are more popular, as are specialisations like radiology, rural areas and general practice less so).

And of course, many of the social charge reductions which are granted to companies for low wage workers end up reducing the revenues of Sécu - this is supposed to be compensated for by the general budget (as it is part of employment policies and not social security) but it's not always done in full. In fact, some calculations show that the full amount of the deficit of the Sécu is due to non payments by the government of amounts it should have. It changes nothing in terms of overall levels of public spending, but it does matter as regards how the holes are plugged - ie by reducing coverage of healthcare for the general population, increasing (regressive) social security contributions) or increasing (more progressive) general taxes...

In the long run, we're all dead. John Maynard Keynes