In the extended edition of Two Towers they show him in a flashback of Gondor retaking Osgiliath.
It's not a particularly flattering portrayal- the military success is shown as belonging to Boromir more than Denethor- but at least it shows him sane.
FEHB plans would also have this incentive. I think at least historically Federal employees didn't switch employers as much (though job-hopping between agencies happens), but more importantly if you retire from the Federal government you keep your health insurance.
There was a discussion about this on another HN thread today. [0]
As you've said, the contact is with the police force not with the individual officers, who get paid the same as they would for any other duties.
There was a whole court case [1] about when the police could charge for this sort of coverage, which codified the current arrangement that, at football matches, they can charge for the officers in the stadium but not for the ones outside it.
In the UK, while police are allowed to have outside jobs, any outside employment must be approved by the force, and as a matter of policy security work is banned. Similarly, security guards aren't allowed [2] to be special constables (people who work as part-time unpaid police officers).
I don't know if (then state-owned) Air France did.