A book I was reading made brief mention of French noblemen who left France to join the Crusades during the mid-16th century, implying I presume, that they joined the Knights of Malta. But at least in pop history, we think of the Crusades as a thoroughly medieval phenomenon, and Wiki at least defines ,"the Crusades were a series of intermittent military campaigns in the years from 1096 to 1487", so again not a phenomenon of the Early Modern Era.
So, the main thing I was wondering then is how the idea of a continuing Crusade against, presumably, the Ottomans, was conceptualized in that period. I'm especially interested specifically in the French perspective, as it was also noted that France itself maintained relatively good relations with the Sublime Porte, so while individual Frenchmen might be heading off to fight the heathens, it seems that France itself was not a part of this. But France aside, I'm also quite interested in the concept as a whole within the Christian world of the time.
A reply to /u/Goat_im_Himmel
Unfortunately I can't answer specifically for France, I leave that to early modern experts on france such as /u/DonaldFDraper . But on the Habsburg side, which included Portugal, Spain, much of Italy, Germany, and the Balkans, the idea of a Crusade against the Ottomans was a major, major deal.
The Kings of Spain, starting from Charles V, had to contend with a rising Ottoman power in the Mediterranean, culminating in the Victory at Lepanto by a coalition largely controlled and funded by Philip II through his half-brother Don Juan of Austria.. The Spanish Habsburgs were able to continue to earn income from the cruzada tax that was promulgated by the Pope, which contributed not much less than their income from the Americas.
The Spanish Habsburgs maintained galley fleets in order to secure the Mediterranean between Spain and their holdings in Italy, including sponsorship of the Knights of Malta. This link was important as grain trade was run this way, as was military lines of communication that ultimately linked Spain to Milan to the Low Countries.
It was a constant battle between them and forces of the Barbary pirates nominally under Ottoman control. We know that the ongoing security concerns contributed to the suppression and eventual expulsion of Moriscos.
Charles V and his successors in Germany/Austria through Ferdinand had to contend with the Ottomans in Hungary. Some authors have pointed out the importance of Hungary, as Ottoman control of Budapest meant they controlled the riverine ways just a short distance from Vienna itself. So from the Habsburg side it was a constant state of readiness even when there is theoretical peace with the Ottomans. Mercenaries such as the Senj Uskoks fought wars of raids and insurgencies constantly. Military orders sent knights to fight in Hungary, or to train there.
As I wrote here, this had an impact with the Reformations of the 1500s. Lutheran German nobles and knights -- in particular in Low Austria, Bohemian lands, and southeastern Europe -- extracted religious and political concessions such as Ferdinand's secret clause in the Peace of Augsburg to keep them in support of the Habsburgs against the Ottoman threat. Archduke Charles lamented, The Turkish threat is a blessing to the Protestants: if it were not for that, we would be able to deal with them in a very different way.
Finally, the Ottomans did invade Italy in Otranto although it was not clear what their strategic plan was.
So the idea of a Crusade was very real.