The great French historian Jules Michelet (1798-1874) sympathized with the French Middle Ages and with the Revolutionary epoch in France, yet he wrote his best work on the despotic French monarchy, which he despised.

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To understand why Jules Michelet, a historian known for sympathizing with both the French Middle Ages and the Revolutionary epoch, wrote his best work on the despotic French monarchy, we can look into his background, interests, and motivations. Here's how you can approach it:

1. Research Jules Michelet's life: Begin by exploring Jules Michelet's biography to understand his personal experiences, education, and the intellectual environment he was a part of. Look for key events or influences that shaped his views on French history and politics.

2. Study his works: Read some of Jules Michelet's notable works to gain insights into his perspectives and ideologies. Analyze how his views on various historical periods, like the Middle Ages and the Revolutionary era, are presented in his writings. Examine the themes and arguments he explores in these works.

3. Identify factors that influenced his writing: Consider the political, social, and cultural milieu of Michelet's time. Look for any historical events or movements that may have influenced his views on different periods of French history. For example, the political turmoil of the French Revolution and subsequent restoration of the monarchy might have played a role in shaping his perspective on despotic monarchies.

4. Examine contradictions and complexities: Evaluate the inconsistencies or tensions apparent in Michelet's views by comparing his sympathy towards the Middle Ages and the Revolutionary epoch with his critique of the despotic French monarchy. Look for any explanations or justifications he provides for these contradictions within his writings or in his letters and correspondence.

5. Consider his historical analysis and interpretation: Assess Michelet's historical methodology and approach to gain a deeper understanding of his work. Explore whether he employed a more critical lens when analyzing despotic monarchies, seeking to understand their impact despite his personal disdain for them.

By conducting this research, you will be able to form a comprehensive understanding of Jules Michelet's motivations and the reasons behind why he wrote his best work on the despotic French monarchy despite sympathizing with other historical periods and the Revolutionary epoch in France.