I can only speak for France, but early modern French culture was extremely captivated both by the protection of their rights and liberties, and in identifying conspiracies that were seen as threatening these liberties.

To answer the first question, Voltaire was feted as a hero on his return from exile in London precisely because he was seen as somebody who had advocated the rights and liberties of other people and been punished for it. Many other roughly contemporary French thinkers were extremely concerned with the codification and protection of rights (Montesqieu, for instance) but Voltaire is the best example of a concern for rights being broadly popular, not just a concern of the wealthy literate elite. Similarly, the war in America was very popular (at least until the bill showed up) because it was portrayed as a righteous war for the rights and freedoms of the American people - when Lafayette returned to Paris he was feted, not just by the aristocracy, but by ordinary Parisians, who saw him as a crusader for individual liberty.

Regarding conspiracies, again, very much so. The French were constantly suspicious of threats to their liberties, both internal and external. It would take a very long time to outline every single one, but probably the most famous and easiest to read further on (if you're curious) would be the Affair of the Poisons, in the late 17th century, when a group of wealthy noble courtiers were accused of being part of a Satanic conspiracy to gain control of the King and plunge France into some kind of dictatorship. Much later, fear that aristocrats would starve peasants in order to stop them from protesting for their rights motivated the Great Terror.

Sources: Anne Somerset's 'The Affair of the Poisons' Jack Censer in 'Press, Politics and the Public Sphere in Europe and North America, 1760-1820'

I also thought that I detected a fixation on conspiracies, specifically the specter of "popery". My question is, are these perceptions correct?

The Whig party originated in the struggle during the later 1670s to prevent Charles II's Catholic brother James, Duke of York from inheriting the throne. In Whig eyes, 'Popery and Arbitrary Power' (i.e. absolute monarchy) were inextricably linked and if James succeeded the throne he would become as powerful and despotic as Louis XIV of France. They were also suspicious of Charles' religion and his relations with France. Were they justified?

Yes. In 1670 Charles signed the clandestine Treaty of Dover with France in which he pledged to wage naval war against the Protestant Dutch Republic while France attacked it on land. He also promised to publicly convert to Catholicism and accepted 2 million crowns from Louis "to aid him in this project" (i.e. Charles would not have to rely on taxes raised by Parliament, which was filled with militant Protestants). In the event, Charles did not convert to Catholicism until he was on his deathbed but he did wage war against the Dutch, though this was a costly failure and Parliament forced him to abandon it.