Pornocracy doesn't seem that easily to achieve or maintain as a government, be it in France or another country... That a King has a mistress is one thing, that the mistress gains political power is another. What a King does in his bedroom is not the concern of the court or the people but what he does in Politics is: there will forcibly be people that will find the situation untolerable and try to solve the problem one way or another.
Plus, if you really want that king of regime to hold, you need the maitresse-en-titre of the current king to choose her successor for the next one: a son generally doesn't want the mistress of his father, especially if she's older than him. The only case I know about a mistress staying with two succeeding kings is Diane de Poitiers, who had been a mistress of François Ier before the latter got bored with her and gave her to his son Henri II. But Diane was never the maitresse-en-titre of François Ier...
One last thing is that mistresses tend only to be linked to "bedroom matters" or to be "companion of the King" when they do no longer share the same bed (Mme de Pompadour always remained the maitresse-en-titre although she no longer slept with Louis XV). I do know that France had a bunch of Kings who were womanizers (François Ier, Henri II, Henri III, Henri IV, Louis XIV, Louis XV) but few of the mistresses really had any influence on politics: Mme de Maintenon & Mme de Pompadour are the only exceptions I see personnally.