I've read John McPhee's *liberty or death * and listened to the revolutions podcast but I'm still unclear about why there was never any Royalist uprising from within the French army.
I understand that there was a fear of the army crushing Paris early on, a whole lot of French officers ended up emigrating and that problems with Bourbon loyalties in the army, like officers say wearing a Bourbon uniform, was a common problem from time to time long after the assembly took control of the country but the army never led any kind of armed revolt.
Eventually the problem solved itself as the army became filled with post revolutionary soldiers but I don't understand why no general ever successfully martched on Paris before then.
(Dumouriez is the only attempt I remember but this is quite late by thinking. Why not earlier than him.)
There are a range of factors that should be called out to answer your question, but here are two:
Firstly, by mid-1792 the army was disorganized and ill-disciplined. The emigration of thousands of officers had resulted in the depletion of many royalist supporters within the army's leadership, especially after the Flight to Varennes. With the regular troops increasingly radicalized by the ideas of the revolution, and with the officer corp increasingly revolutionary (through the process of royalists leaving the army), it would be difficult to muster the forces required to march on Paris.
In saying that, Lafayette did try. After the initial defeats of April and May 1792, Lafayette proposed an armistice to the Austrians and sought to close the political clubs of Paris. After the events of the 20th of June (which saw the palace invaded and the King threatened by a mob), Lafayette went further. Leaving his troops (and opening himself up to the accusation of desertion), Lafayette returned to Paris and implored the Assembly to close the clubs, curb the press, and ban petitions. In particular, Lafayette attacked the Jacobin Club for producing the nation's instability and jeopardizing the revolutionary project (ironically, Lafayette had been a founding member of the club).
"I beg the National Assembly to order that the instigators of the crimes and violence committed on 20 June in the Tuileries be prosecuted and punished as criminals for lèse-nation, and to destroy a sect that infringes sovereignty and tyrannizes citizens, and whose public debates leave no room for doubt about the atrocity of the plans of those who lead it." - Lafayette, 28 June 1792
Fearing a coup, Lafayette was denounced as a traitor by the Jacobins (both the Brissotins and the Montagnards), with Robespierre demanding his arrest. Lafayette subsequently tried to rally the National Gaurd of Paris (which he use to command), but they rejected his pleas as well (Since his initial command, the guard had admitted passive citizens, further radicalizing the revolutionary body). Retreating from the capital, the increasingly powerless general tried to organize the King's escape, but to no avail.
One interesting point to note is that the royal family seemed to do little to help Lafayette in his attempt to suppress the radical forces of Paris. Historian Simon Schama questions if the royal family was over-confident in their position (given their belief allied forces would rescue them), while Historian Christopher Hibbert states:
But the reaction was short-lived. The court did not take proper advantage of it, the Queen, in particular, being wary of accepting help from those whom she considered untrustworthy or dislikeable. ‘She was more intent upon appearing to advantage in the midst of the peril,’ Lafayette later remarked with some bitterness, ‘than in averting it. As for my relations with the King, he always gave me his esteem, but never his confidence.’ ‘Better to perish,’ the Queen herself said, ‘than to be saved by M. de Lafayette.’
As a result, the failure of the French Army to save the King is a result of a multitude of factors. After Varennes and the initial defeats of the war, reliable troops were hard to come by, as were officers willing to lead them. Furthermore, distrust between the court and liberal monarchists (such as Lafayette) prevented cooperation and coordination, hampering efforts to save the King.
If you're looking for a French Revolution podcast that emphasizes historical debate and ambiguity, be sure to check out 'Grey History: The French Revolution'.