Every time the army at least tried to stay loyal to the government, not openly siding with the people or popular risings.
So that in itself is partial proof that the Army would be willing to support the Government against the mobs.
It's a proof that they held their privilegied position firmly, and that they were ready to fight for anyone granting them. As the people responsible of the uprising in first place, a mix between liberal intelligentia and popular classes, had as an unclear objective the set up of a republican government, it was a threat for them.
But with Louis-Philippe arrival, I should say planned arrival, they recieved guarantees.
So loyal to government, yes. Loyal to the dynasty and the king, far less.
And that is for the faithful elements. If the best we can say about is "At least they didn't joined the revolutionnaries", it's not what I could call "a blind devotion".
And yes 4 days isn't enough for a nation-wide revolt but at the same time the fact that there was no major disturbance's period proves my point.
No major disturbance during the period?
-1817 : Affaire Fualdès in Aveyron.
-1819 : Vienne uprising
-1820 : Duc of Berry murder, riots in Paris, tenative of plot within the Paris garrison
-1822 : Berton Plot, Troubles of Ecole de Droit, Quatre Sergents de La Rochelle Affair
-1824 : Ordinance of 7 December that put out the army ancient officers almost all from Napoleonic period, troubling the army
-1825 : "Loi du Milliard" that mark defavorably the public opinion
-1827 : Political struggle against the reinforcement of censorship, Funeral of Manuel with 10 000 persons following the corpse, Dissolution of Garde Nationale
-1830 : July Revolution
-1831 : Riots of Febuary, Canut Revolt
-1832 : Riots during Lamarque funeral
-1834 : Canut Revolt, republican riots in Lyon and Paris, Fieschi attentat
-1836 : Plot of Bonaparte to realise an uprising of Strasbourg garrison.
And that's only for the ponctual events.
I can only advise you the
"Histoire de la restauration et des causes qui ont amené la chute de la branche ainée des Bourbons" that is a contemporary and relativly faithful account of the situation (being legitimist himself, there's little suspicion about a negative bias)
Now, yes urban centers and Paris especially had an important political role. There's many reasons : a huge centralisation that meant that any tentative to throw away a government had to happen there.
The population expected by some habit, and maybe because of what was called "contagion de l'obéissance" (obeyment epidemic) that was basically the result of recent political experiences (on this order of idea : tone down such idea or you'll be in real trouble) that explain a certain wait-and-see policy reinforced by said hypercentralisation.
"The Parisian insurrection is the climax of a more diffuse and deep crisis [...] going from [...] institutions for defense of censive freedoms, to see the people and the republicans of the town hall uprising with barricades covering street and parts of Paris"
Even saying that province is apathic in 1830 is wrong :
"The crisis isn't only a Parisian affair. French episode of 1830 revolutions, it is also economical and social, as provincial troubles demonstrate. The industrial crisis of 1825, then a livelihood crisis in harvest's year 1827-1828 increase the difficulties and frustrations that, in province, explode at news of Parisian riots : hunger riots, winemaker riots against tax agents, "rats de cave", foresty troubles, destruction of mission crosses, municipal revolutions, are as much answer to power's vacancy"
From "Les dernières monachies en France (1815-1848)" in "Le XIX° siècle", under the direction of J.L. Robert.
And of course, I repeat myself, 4 days of uprising aren't going to launch a united nation-wide revolt. That's novel stuff, not History. It does not show an "apathic" population but it is at contrary totally normal : how French Revolution happened in first place is the exception.
And to the army situation, it might not. Keep the Royalist units at home and the regiments with questionable loyalty would be sent to Algeria. It deals with two birds with stone. You get rid of a potential threat and gain a foreign victory.
When the decision was made to send an expedition in Algiers, the situation was already really tense. Sending the bad elements in Algiers meant having the possible risk of a mutiny and the refusal to fight.
You just can't give an army the possibility of doing that if you value your power.
As to the National guard, really that was one of the stupidest moments in Charles's reign. He should have disarmed the guard but not dissolve it. Or done both, disarm and dissolve. But leaving a potential threat fully armed was very short-sited and dumb.
He could have tried to disarm, but not without dissolving : the whole point of Garde Nationale was to be armed.
Now, he could have successfully disarmed it, but it would have a cost politically : at this point the liberal and republican influence was already strong and you had an entiere campaign to disnounce the reduction then dissolve of the guard. As it was really limited in numbers and training, it was calculated that letting weapons on the loose (and honestly, after the Napoleonic wars, you had already plenty on the loose even if of less quality) was not worth the risk of a possible uprising of part the guard (
a limited part, of course, but disastrous politically).
Or they could launch an actual siege of Paris, like in the Franco-Prussian war
Not possible in this context : "La Garde Nationale : une force politique ambigüe"
(p 246) summarize it well
"Ordinances having been preparated in the greatest secret, no real mesure for maintain order was planned. Only the 27 July, the Maréchal Marmont, major-general of the Royal Guard, recieved the supreme command of the 1st military region. Disposing then of 13 000 men including 750 cavalerymen : five uncomplete regiments of Garde Royale, including two swiss, and four line infantry. Gendarmerie regiment was still under the Police prefect authority.
Began in improvisation, a timid and loose defense encouraged the insurgents. Laws on mobs dispersion were obsolete, and the ordinance of the 28 july putting Paris in siege made them useless. It had for results to slow the repression forces, then to exacerbate their reactions."
The page 247 is lacking there, but it's saying the line infantry was spared by insurgents (that took the advantage of action) and that it eventually passed to insurgent side, forcing Marmont to plug the holes where it's most needed, but eventually stripped whole zones of needed forces.
To resume it : the whole thing was poorly planned (if planned at all) from the beggining, as a consequences of Charles X policy (and not something accidental he could have easily removed by wandhaveing), and given the centralisation of France, the likely loss of Paris meant the loss of the state eventually.
The comparison with the siege of Paris doesn't really works there. First, if you're arguing that the situation is too different between 1810's and 1820's, what to say about this chronological difference?
Second, we're talking of a defeated, occupied country with urban uprisings while the mass of population wants most of all peace; compared to a situation of a political, social and economical disorder without invading army and with an army that actually showed that it could pass to insurgents.
Also, if it drags on we could see an intervention by the Concert of Europe. I think Austria and Prussia would be willing to send troops to aid the French rather then risk a revolutionary regime.
It's possible, but they recognized quickly Louis-Philippe takeover (his takeover being pretexted precisely for this reason).
I would point, however that they didn't acted against Belgian Revolution, while Austria and Prussia were favourable to maintain Belgium into the Kingdom of Netherlands, mainly because the United Kingdom didn't wanted so.
I think that an intervention on France, that didn't seem to have been really envisioned even during the immediate aftermath, would have encountered the same issues : London wasn't too keen about a revolutionnary regime in France for sure (while I think it would have turned quickly as the OTL Second Republic) but clearly wanted to preserve the balance of forces.