Why has France had so many more revolutions and changes of government than most of its neighbors?

I'm traveling and away from my books right now so can't provide direct text citations, but I'm happy to recommend a number of sources for further reading if people have questions.

One thing that's important to emphasize first is that France's (very real) see-saw history of revolutions and coups since the 18th Century might seem more dramatic than it is because France itself has been a polity capable of having regime changes over that entire time. That can't be said for many of France's neighbors, especially Germany and Italy, which only became countries in the middle of the 19th Century.

If you date things from 1871, then France has had a parliamentary republic (the Third Republic), a dictatorship (Vichy), another parliamentary republic (the Fourth Republic) and a presidential republic (the Fifth). In that same time, Germany has had a constitutional monarchy (the Empire), a republic (Weimar), a fascist dictatorship (you know) and a split between a parliamentary republic and a communist dictatorship. Depending on how much of a line you draw between the Fourth and Fifth republics and how you count the division of Germany, the two countries are basically on the same level when it comes to constitutional change. Certainly France isn't an order of magnitude less stable. In the 1789-1871 period, the maps of Germany and Italy were completely redrawn multiple times. Most of those don't count as regime changes because it wasn't a single state changing its form of government, it was a change in the state.

That said, France was really unstable in the 1789-1871 period, which saw it go from an absolute monarchy (the ancien régime) to a constitutional monarchy (the early period of the French Revolution) to a parliamentary republic~~ (the Constitution of 17~~93 early stages of the First Republic), a directorial republic (which I now know is a thing), an... autocratic republic, for lack of a better term (the Consulate), a constitutionally absolute monarchy (the First Empire), a constitutional monarchy (the Restoration), a different constitutional monarchy (the restored Empire of the Hundred Days), the prior constitutional monarchy again (the Second Restoration), a more liberal constitutional monarchy (the July Monarchy), a presidential republic (the Second), a constitutionally autocratic monarchy (the Second Empire), and a self-appointed government of national defense before the Third Republic was finally established. That's pretty chaotic, but the pace of change did slow down dramatically after 1815. The years 1789-1815 saw a new form of government (by my schema, which is off-the-cuff) about every three years. From 1815 to 1871, there was a new form of government on average every 11 years. (Since the establishment of the Third Republic France has had a new form of government on average every 37 years.)

So what you're looking at is three periods:

The utter chaos of the French Revolutionary period
The unstable regimes of 1815-1871
Relative stability from 1871-present

What caused these changing degrees of stability? I think the most important aspect is a question of legitimacy. Enduring in power can be self-perpetuating — merely by continuing to rule and not being completely terrible at it, people get used to a system of government as the status quo. So you've got a chicken-and-egg problem: the early French governments didn't last long because they were unstable; they were unstable because they didn't last long.

There are lots of reasons why the French Revolution was so chaotic; I'll let that largely pass for now since my focus is France after 1815. One thing I will highlight is that a major effect of the French Revolution was a centralization of the French state. Ironically, though Louis XVIII's powers were formally constrained in a way Louis XVI's never were before 1789, his capacity to enforce his government's decisions on France were considerably greater. One consequence of this is that control over the central state was a much bigger prize than it may once have been, and often all you needed to control the state was to control Paris, from which the state was run. And one definite legacy of the French Revolution was an increased political consciousness among the people of Paris, who would topple governments in 1830 and 1848 and try to in 1832, 1848 (again) and 1871.

Another factor is that very few of these governments were actually based on universal manhood suffrage. Every 19th Century French government from 1789 on had elections of some sort, but most of them severely limited the electoral franchise to wealthy property owners. This limited the number of French people who had voted for, and thus had a stake in, each regime. When the people of Paris toppled Charles X and then Louis-Philippe, there were no significant mass uprisings of royalists in the rest of the country, unlike what had happened after Louis XVI's execution. It's probably not a coincidence that the two longest-lasting governments of this time period, the Second Empire and the Third Republic, both had universal manhood suffrage.

So why did the Third Republic finally stick after all these years of chaos and turmoil? As it happens, I've written an essay on that exact topic. The first elections after the fall of Napoleon III actually returned an assembly with a firm majority of monarchists. But these monarchists never managed to restore the monarchy because they couldn't agree on which monarch to restore! About half the monarchist delegates were Legitimists who supported the House of Bourbon (descendants of Charles X); the other half were Orléanists who supported the House of Orléans (descendants of Louis-Philippe). For a variety of reasons, including the stubbornness of the Legitimist heir over the matter of the French flag, the two sides were never able to come to an agreement. Rather than have a monarchy with the wrong monarch, both stuck with a republic as a temporary expedient. Except as the Republic lasted, it built up legitimacy, and then out-and-out republicans started winning elections. (Also important: even as the monarchists couldn't agree, the different factions of republicans managed to set aside their differences to preserve the Third Republic, rectifying a key failure of the Second Republic.)