The eighteenth century saw a dramatic renewal of ancient ideas of republicanism and democracy (Latin and Greek originated works of course), but that came in the late eighteenth century. The American Declaration of Independence in 1776, the French Revolution of 1789, and the Haitian Revolution of 1791 are the important moments in complex ways which I will not attempt to cover here. The one thing to be noted here is that ideas of republics certainly attracted attention before these events, which are hard to imagine without the influence of those idea, but not in the sense that anyone would have expected the centre piece of the British Empire, the premier nation in Europe, and the centre piece of French colonialism in the Americas to have so dramatically followed through on them.
The idea of democracy was even more anachronistic looking before these events, which in any case did not lead to full implementation of democracy and certainly not its normalisation, but did take steps in that direction. Earlier in the eighteenth century, even Rousseau did not think of democracy as the ideal. Even allowing that his advocacy of elective aristocracy is in accord with representative democracy, it does not look as if he expected republicanism to sweep through Europe. His text on a constitution for Poland was for an aristocratic state on the verge of extinction as Prussia, Russia, and Austria arranged its complete partition between 1772 and 1795. It was not a model for European republics, nor was it any more democratic than the existing aristocratic commonwealth with a limited monarchy. Montesquieu, Smith and Hume looked upon republicanism as a form of government appropriate to liberty, but not as necessarily superior to monarchy, and maybe less desirable than monarchy in the circumstances of most modern states.