A couple of points I would make to start off with, firstly, I would not agree that those in positions of power never held sincere religious convictions in the early modern period, quite the opposite. Some certainly used religion in cynical ways, that's definitely true, but many kings and aristocrats were also deeply religious. For example, a number of nobles in Britain chose to lose their heads for their Catholicism (or burn for their Protestantism), which is not the behaviour you would expect of insincere believers.

Secondly, its worth underlining that the process of Reformation was very different in different places, and it was not always the case that it strengthened royal authority. Reformation usually increased the power held by someone, but that wasn't always the monarch, in other cases it might be clergy or nobility.

For example, while the English Reformation was centred around the monarch and served to centralise power, in Scotland it was basically the opposite. Reformation in Scotland involved the nobility acting to bind the monarch to a model of reformed Protestantism and in the process, restricting their authority by portraying their monarchy as 'legal and limited'. This involved a series of 'Confessions', documents which embodied the king's duty to Protestantism and the subject's loyalty to the king on condition of meeting these duties, which in practice the king had little choice but to go along with.

These competing versions of Reformation would be part of the reason that the British Isles fell into civil war in the 1640s, due to the contradictions caused by Charles being both the 'Godly' monarch of England and the 'legal and limited' monarch of Scotland. The first fighting of these wars, and the reason Charles so desperately needed money from Parliament, was caused by Scotland resisting English attempts to reform the Scottish church, which involved them rallying around a new version of the Reformation-era 'Confessions' known as the National Covenant. So essentially, while Reformation did strengthen the English monarchy in the 16th century, it also weakened it in the 17th century after the Union of Crowns as a different form of Reformation was introduced from Scotland.

So basically what I'm trying to caution is that it wasn't ever really as simple as monarchs having an easy path to greater power via Reformation. That said, it obviously was still something that did happen, and your question is still a valid one, which I will try to answer now.

Essentially, there were three main European powers who remained 'officially' Catholic, Spain and Austria (who were at various points linked as part of the Hapsburg Monarchy), and France. Now, I do not know a great deal about Spain or Austria, so I wouldn't feel confident in discussing the nature of the strength of the Catholic church there, though in a casual sense its common knowledge that the Catholic church has been extremely strong in Spain for a long time so to me it isn't really surprising that Spain resisted Reformation.

France, however, I do know a reasonable amount about, and is a very interesting case. France underwent devastating Wars of Religion in the 16th century which involved both sincere religious conflict and a huge amount of political manoeuvring. The fact that France remained a Catholic kingdom at the end of the wars is not really the result of choices made by its monarchs, so much as it was the result of France's powerful Catholic aristocracy, who formed what was known as the 'Holy League' to uphold Catholicism. In fact, the league assassinated a French King, Henry III, because he was attempting to establish Henry of Navarre, a Protestant, as his heir. On his deathbed, he apparently told Henry of Navarre that the only way to establish peace was to convert to Catholicism, which he did, becoming Henry IV of France. Despite ostensibly having converted, Henry IV enacted the 'Edict of Nantes' which provided toleration for Protestants, however, he was ultimately also assassinated by a Catholic fanatic.

So in France, the answer is essentially, some tried, but did not succeed. However, France also ultimately became something of a special case in that while it remained Catholic in some senses, its monarchs often did not answer to the pope in the way one might expect of a Catholic monarch. In the Thirty Years War, for example, France fought on the 'Protestant' side, for strategic reasons.

In the reign of Louis XIV, this idea of a France which was 'Catholic but independent of the pope' became officially codified in the 1682, Declaration of the Clergy of France, which enshrined the idea of Catholic French church that did not involve subordinating monarchical power to the pope. This became known as 'Gallicanism', and I have read arguments that this also served as the model on which James II of England and VII of Scotland hoped to impose a 'tolerant' form of Catholicism on the British kingdoms, where loyalty to the king would be elevated above confessional concerns. However, how this would have gone is hard to say as his experiment was cut short in 1688 as he was deposed, due, in part, to his lenient attitude to Catholicism.

So basically, in a simplified sense, the French monarchs did ultimately manage to solidify their authority in a similar manner to the English Reformation, but did so without officially renouncing Catholicism.