Ask Lemmy

Not an historian, but to give some ideas, the Enlightenment thinkers were "progressive" nobles and bourgeois who succeeded without noble's privileged and obviously could explain why the system is unfair. It's tempting to have the romantic image of the little people rising by themselves, but it is not illiterate farmers that could have wrote about the philosophy of governance.
Voltaire had a lawyer father (bourgeois) and a low rank nobility mother.
Rousseau was born in the Republic of Genova (oligarchy with elections) of watchmaking family (bourgeois).
Beaumarchais was also the son of a renowned watchmaker (bourgeois).
Diderot was the son of a knife maker renowned for surgery blades (bourgeois).
D'Alembert was an abandoned child but taken care of by a knight (~noble privileges).
Montesquieu was from high nobility with administrative responsibilities (noble).
Lafayette was from military nobility (noble).

Another important point is that the early thinking was to promote an enlightened monarch, highly educated and aware of the issues of his people, so he could be a perfect leader for the people with some limitations and power balance. Some monarchists today still promote this kind of ideal. There was probably not too much problem to talk about better education in those salons and sharing more power with the other educated people.
Thinking about ending the monarchy came later and the beheading of the king was kind of an interplay of circumstances that was not planned by the early Revolution leaders.