Monarchs across Europe worried about the revolution happening in France, why?

From the Middle Ages onward, much of Europe operated under the feudal system. In feudalism, the king owns all of the land in his kingdom but gives large parcels of it to nobles to rule in exchange for military service. The nobles then designate smaller portions of land to be lived on and worked by the peasantry, who are in turn protected by the nobles. The kings and nobles, along with the peasants, represent two parts of the Three Orders of society: bellatores (those who fight, the nobles) and laboratores (the working peasantry.) The third Order was oratores (those who pray,) including all of the religious monastics and clergymen in society. These Three Orders were considered to be the natural forms and functions of a society, and as long as everyone fulfilled their role, everything was perfect... right?

Not so much! The feudal system became increasingly complex and troubled as nobles might break up their land among lesser nobles, often resulting in an individual being obliged to more than one superior! In addition, times of environmental stress created a difficult situation for the peasants. Crop failure was considered to be the fault of the peasantry (or punishment from God) while the nobility were still demanding a significant portion of the food produced. Peasant riots shared the same sentiment which later drove the revolution.

Here is something important to bear in mind: though peasants were not skilled in the arts of war and diplomacy, they far outnumbered both the religious and noble of society. As the feudal system continued to disintegrate or become more convoluted over time, it made things harder on the largest portion of society. Pretty much across the board, life for the peasantry was the same in every kingdom: survive on meager foods and work until you die. When the French peasantry became fed up with being exploited under the Ancien Regime, which developed out of feudalism, it signified a possibility that was previously unthinkable: the peasantry could overcome the nobility. 

Monarchs across Europe were rightly frightened because their power in society, and the entire way their kingdom functioned, developed out of the feudal system and likely suffered the same complications as in France. The combination of social inequality and increased education and literacy for the peasantry proved deadly for many a noble. Scholars like Marx and Engels later described these revolutions as the naturally occurring result of an unsustainable socioeconomic system which exploits the proletariat (working class) and impedes human development. Perhaps the monarchs of Europe heard of the Revolution in France, took a long look at their own kingdoms, and realized that they, too, were unsustainable.