I have been listening to Mike Duncan's Revolutions podcast about the French Revolution. I strikes me as odd that every time the government was overthrown the army simply accepted the new management and got on with fighting the Austrians, British, Spanish, Prussians, other Frenchman, etc.
The army does not seem to have remained loyal out of ideological devotion, because over the course of the Revolution its membership ran the gamut of political demographics including noble officers, foreign mercenaries, common-born officers, bourgeoisie active citizens, patriotic sans-culotte volunteers, and levee en masse peasant conscripts. Similarly, the government went from feudal monarchy to constitutional monarchy to republicanism to angry-mob-breathing-down-the-legislatures-neck-ism to ultra-leftist bureaucratic despotism to reactionary kleptocracy to Napoleon. The army probably wasn't loyal to money because the harvests kept failing and the economy kept crashing. The army probably wasn't loyal to government favoritism, because representatives on mission kept executing their commanders and micro managing them into dangerous hyper aggressive tactics. It's problematic to argue that the army was devoted to an abstract notion of national identity because they were busying slaughtering members of that shared national identity in the Vendee and Federe uprisings. In fact, the Federe uprising is an interesting counter example because iirc the French Navy joined the harbor cities in revolt against the central government. It's hard to argue that the army was loyal to the constitution because the constitution was at various times being invented, rewritten, suspended, restored, amended, suspended again, and Napoleon-ed.
In the midst of their employers purging each other, their families starving, their citizens revolting, their enemies swarming, and in general all hell breaking loose, the French Army kept fighting. Why?
edit: I don't know how or why my post title has been flaired with DEATH. What is it and how do I change it?
It's kind of an oversimplification to talk about "The French Army" as one clearly-defined body, especially during the Revolutionary period. I'm not strong on the actual Revolutionary period, but for instance, the Paris Commune saw French troops, under the authority of the Versailles government, slaughter the French troops of the Garde Nationale - basically a citizen's militia that was one of the driving forces of the Commune.
It's also not completely true that the army always remained loyal to the government in place. The Hundred Days (Napoleon's "comeback") saw the army declaring for him against Louis XVIII. After Waterloo and the "White Terror", the army was purged, with numerous highly-ranked commanders imprisoned or executed (most famously Ney).
You have some misconceptions about the french history. I.E, the french monarchy was not feudal at all during the XVIIIth century, it was an absolutist monarchy which is the complete opposite. There are many reasons why the french army was loyal, the main reason is that only the main officers were involved in the political stuff in Paris, the simple grunt was just concerned about receiving his "solde", food and clothings before the next battle. But this is only true for the frontline where the army was busy and far from the capital. In Paris, there were many coups and the army was involved in these coups. The general Bonaparte became consul in 1799 after a coup with the help of the troops of Murat so saying that the army was loyal is true for the frontline but not true in Paris. It is also good to remind that the general Bonaparte was sent to Egypt with his troops because he was a well known jacobist and very popular, so the Directoire hoped to get the rid of him before he got rid of them.
Flipping the question on its head a bit, the French Army was actually quite mercurial in its support of the Revolutionary governments. It is important to distinguish between support for the Revolution and support for Revolutionary governments. While a number of officers and men owed their rise to prominence to the Revolution's opening up of the ranks and the various wars gave them continual employment, this did not translate into an automatic support for those in power in Paris. Instead, the continued existence of these various armies in the field meant that the Revolutionary French Army became an institution in and of itself, and many of its officers and ranks owed their allegiance to it and not the various Republics.
The tensions between Paris and its military were quite persistent throughout the various Revolutionary period. But although the Army was subject to periodic oversight and interference and officers were cashiered or killed for too close a connection to Jacobinism after Thermidor, the Army as a whole was not as subject to the various regulations as other components of the French state. Paris increasingly needed its military because of the various wars. As French arms began to export the Revolution into foreign areas like Italy, the Low Countries, and Central Europe, military commanders began to operate in a semi-autonomous fashion. Napoleon was a case in point of the semi-autonomy French generals possessed. He conducted his Italian campaign without much consultation with Paris, and actually forced the ratification of the Treaty of Campio Formio while the Directory wanted a more prolonged negotiation.
Many of the plotters within the Directory recognized that the Army was a semi-autonomous political institution within the French body politic. As such, they often actively courted the support of various generals in their political scheming. Although Napoleon was the figure who climbed atop this greasy pole, he was only one of several popular generals that various conspirators within the Directory were hoping to use to kill off the existing French government. Emmanel Sieyès, one of the key plotters in Brumaire, would famously quip, "I need a sword," in other words, a man who could command the loyalty of one of the few powerful institutions that possessed a great deal of popular legitimacy within the Republic, the army. Bernadotte, a general and Minister of War, was the favorite of the Neo-Jacobin factions that wanted to reestablish the Revolution's leveling tendencies. Jean-Baptiste Jourdan toyed around with many different factions. Lazare Hoche, who enjoyed almost as much fame as Napoleon had unfortunately died of tuberculosis before Sieyès's initial soundings towards him could bear fruit. Jean Moreau, the youngest general in the army, refused to compromise himself with politics despite entreaties to do so.
One of the foundations of Napoleon's ascent to power was his binding of the French Army to his personalist state. Although Napoleon liked to claim his imperial meritocracy was open to Frenchmen of all walks of life, a firm majority of the new nobility (ca. 67%) were military men. The efficient Napoleonic state was able to make good on its promises of pensions and care for dependents, unlike its Republican predecessors. The exalted prestige and titles meant that many military officers could marry upwards into French elite society. Celebration of military Gloire became one of the cornerstones of Napoleonic civic culture and expanded upon the Republic's valorization of its generals. Napoleon also actively cultivated his image of the age's supreme warlord and state imagery and politics emphasized the intimate connection of the Emperor to his troops. Although the grinding nature of the various wars in Spain and the string of defeats between 1812-14 denuded Napoleon of some of this military support, especially within the Marshalate, he remained a popular figure within the military. The Hundred Days would not have been possible without the support of the Army, which was one of the few social institutions to unambiguously rally around Napoleon.
Sources
Bergeron, Louis. France under Napoleon. Princeton, N.J.: Princeton University Press, 1981.
Dwyer, Philip G. Napoleon and Europe. Harlow, England: Longman, 2001.
Hughes, Michael J. Forging Napoleon's Grande Armée: Motivation, Military Culture, and Masculinity in the French Army, 1800-1808. New York: New York University Press, 2012.
Natalie, Petiteau. “The Nobility of the Empire and the Elite groups of the 19th century - a Successful Fusion.” Napoleon.org. http://www.napoleon.org/en/reading_room/articles/files/nobility_empire_elite_arsenic.asp#ancre3
Woloch, Isser. Napoleon and His Collaborators: The Making of a Dictatorship. New York: W.W. Norton, 2001.