Obviously, I refer to it as a conspiracy as in made-up things. In the Medieval era, Jews were scapegoated for harvest failures and diseases. Yet as they lacked substantial power, it would have been ridiculous to claim that they rule the world. Industrialization and capitalism expansion gave a pathway for Jews to excel with aforementioned Rothschilds becoming the richest family (outside of monarchies) at one point. The Protocols of the Elders of Zion may have crystallized the belief, but I doubt it was the source.
The origins of the "international Jewish conspiracy" can be traced to the Middle Ages. The stereotype of Jews working with money has very real foundations in the ways in which Jews were generally forced to make their living in Medieval Europe. Jews were subject to a whole host of laws and decrees which limited the ways in which they could earn a living. Among these restrictions included prohibitions against owning land, joining artisan’s guilds, selling new merchandise, and even working on Sundays and Christian holidays. These laws were not limited the Medieval period and can be found in the Early Modern Period as well. Frederick II of Prussia issued a charter in 1750 that placed these very restrictions on the Jews of his kingdom.
On its own commercial business was generally not considered troublesome and most Jews made a meager living in some sort of mercantile business. What most non-Jews in European society found morally suspect was moneylending; a profession that many Jews were forced into by circumstance. Since the Middle Ages Jews had been the main source of financial credit to the European populace due to religious prohibitions against Christians participating in usury. Jews were not alone in practicing moneylending, of course Christians engaged in the practice as well. However, they rarely received the same levels of disdain that the Jewish moneylenders did.
So why could Jews not become artisans? Well in order to be an artisan (in the city anyway) one generally needed to join a guild. Guilds, being religious organizations, almost always forbade Jewish members so Jews resorted to forming their own, such as the Barber’s Guild at Krakow in the early seventeenth century. However, Jewish guilds often played no significant role in the economic lives of their members and quite often found themselves in competition with Christian guilds. With farming and crafting out of reach for most Jews, peddling second-hand goods was the most readily accessible form of work available to Jewish men.
At this point, I will focus on late 18th - 19th century France, since I am most comfortable speaking about that region. Most Jewish merchants conducted business with Christian peasants in the countryside and at the marketplace in the cities and many had amassed enough money to add loan-making to their résumé. These Jewish moneylenders played an important role in the rural economy of northeastern France. In a society with little to no banks, Jews provided a ready source of agricultural credit to the non-Jewish peasants. As a result of this the Jewish community was often blamed for the indebtedness of the Alsatian peasantry and their image as recalcitrant and parasitic businessmen persisted throughout the nation. The combined economic tensions and underlying religious animosity fueled popular hatred and distrust that bubbled under the surface of French society.
You mention the Rothschilds, and I am glad you did. The French branch of the Rothschild family heavily invested in building Paris during the Second Industrial Revolution and many Jewish investors poured money into many of the volatile new industries of the industrial revolution (and made a lot of money in the process). Jews in France found themselves integrating more easily into French society at a time when Jewish and Non-Jewish French people were asking themselves if the Jews could in fact be Jewish and French (This was a debate happening across Western and Central Europe). In my opinion, the point when the "International Jewish Conspiracy" hit French society was the failure of the 1870-71 Franco-Prussian War and the economic recession that followed. Anti-Semitic publications such as Edouard Drumont's La France Juive emerged and were very popular (100,000 copies were sold in its first year of publication). Antisemitic publications alleged that Jews across Europe were more loyal to each other than to the nations in which they lived. In La France Juive, Jews are portrayed as "Christ killers, economic vampires, subhumans, masters of France, reptiles dripping with slime and engorged with their victims blood." [Simon Shama, The Story of the Jews (New York: Harper Collins, 2017), 640] The Dreyfus Affair later cemented the idea for the anti-Semites of France that Jews were not loyal citizens and were internationalists. Here are some images published by La Libre Parole in the late 1890s depicting common anti-semitic tropes. Here Here and Here
Admittedly I am less knowledgeable about the impact of The Protocols of the Elders of Zion and would defer to someone more informed on the subject. I can say that it was widely popular and the themes written in it reinforced many of the Antisemitic ideas that were already present in European society. Daniel Pipes writes in Conspiracy: How the Paranoid Style Flourishes and Where It Comes From:
The great importance of The Protocols lies in its permitting antisemites to reach beyond their traditional circles and find a large international audience, a process that continues to this day. The forgery poisoned public life wherever it appeared; it was "self-generating; a blueprint that migrated from one conspiracy to another." The book's vagueness—almost no names, dates, or issues are specified—has been one key to this wide-ranging success. The purportedly Jewish authorship also helps to make the book more convincing. Its embrace of contradiction—that to advance, Jews use all tools available, including capitalism and communism, philo-Semitism and antisemitism, democracy and tyranny—made it possible for The Protocols to reach out to all: rich and poor, Right and Left, Christian and Muslim, American and Japanese.
Other sources: The Jew in the Medieval World A Sourcebook: 315-1791, ed. Mark Saperstein (Cincinnati: Hebrew Union College Press, 1999)
http://exhibits.library.duke.edu/exhibits/show/dreyfus/intro/anti-semiticpress
You may also be interested in my previous answer:
Several links in that answer are also worth clicking for additional context.