Well with 6 schools and absolute monarchy get use to see revolution in France. The solution is either get rid of the king or get rid of the schools, your choice.
I would recommend to change to republic because of the nice bonus to tech it give and the lower class will be easy manageable(no uprising) if your government maintain 40% popularity (if it drop below that just hold an election) The nobles can get tipsy occasionally but they are easily bullied by 500 republicans guards and a couple of cannons.
In my last French game Louis XIV didn't die of old age but of neck trauma. By 1750 i had ~8 schools and had only one pathetic royalist uprising (half stack) that was promptly cut to shred by my republicans guard. When you're advance enough in Tech you can start to replace the schools with economics buildings
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