The return of Napoleon from Elba is one of the most interesting events in history, leading to the March on Paris and eventually the Waterloo campaign.
However, seeing as the return only lasted a bit over 100 days, what was it like for someone in France at the time? How did the population take the news, and did the government institutions get changed from the monarchy ones in that time?
Also, my biggest question: Was there any chance of it being permanent? Britain/Prussia/Russia/Austria didn't take kindly to the return from Elba and immediately started military operations against France, but was it possible for Napoleon to hold it off?
Lastly, was the Hundred Days nothing more than a curious historical footnote in terms of effects? Did it cause anything to be really different than a universe where Napoleon never escaped Elba?
I'm going to try to address this in the order that you presented the questions.
How did the population react to the return of Napoleon, did the government institutions change, and what was it like, in general, for someone in France at the time?
Here's the short answer right off the bat, because this is longest: the public took the news well in general (but not universally) on his return but his popularity flagged fairly quickly, most Royalist institutions weren't changed because most Revolutionary institutions had been left in place, and the question of what was it like for someone in France is pretty complicated.
Now let's pull that apart.
Something that's important to remember is that Napoleon, despite being in exile, wasn't acting in vacuum; he didn't decide that he was going to return to Paris simply because he was sick of Elba, but rather because he'd come to understand that prevailing conditions there favored his return. The First Bourbon Restoration was initially reasonably popular, and even left most of the Revolutionary Period reforms in place; a condition of the Restoration was, in fact, that France have a written constitution, the Charter of 1814. On his return, Napoleon instituted some constitutional reform, but it didn't amount to much.
The issue, as it often ends up being, was one of public relations and which demographics profited by the Restoration. Louis XVIII made several symbolic gestures toward rolling back the reforms of the Revolution, and while acts like replacing the Tricolore or recognizing the anniversary of Louis XVI's death might seem trivial in the present, it really rustled a lot of people's jimmies after everything that had happened. Not everything was so trivial, as some of the King's reforms did in fact amount to a dramatic reduction in the franchise. The return of the Catholic Church to a position of influence in France was a big deal as well, and not just among non-Catholics (who were a major affected demographic), as the disposition of lands owned by the Church before the Revolution (as well as lands owned by other groups dispossessed during the Revolution) became an area of major dispute. There were also groups, prominent among them the army, who were loyal to Napoleon or unlikely to ever support the restoration of the monarchy. All of this was on top of economic problems caused by the economic warfare practiced during the preceding war and the influx of British trade after the war's resolution (this is a topic all by itself, and my actual area of expertise).
So what does all of this add up to? Napoleon left Elba principally because of the unrest caused by the actions of the restored monarchy. Troops sent to stop him joined his march, and Louis was forced to flee Paris in the face of Napoleon's approach. Not everywhere was as thrilled by all of this as the population of Paris, but only La Vendee entered open rebellion, which was defeated in reasonably short order. Popularity of Napoleon aside, it's important to note that the people of France were incredibly tired of fighting: the various wars had gone on for nearly two decades, the population and economy of France was devastated. Ultimately, after losing at Waterloo, Napoleon abdicated and was more-or-less told to leave Paris in the face of a populace that had fairly complicated feelings about the whole affair. After his abdication a small degree of military resistance to the Prussians marching on Paris continued, but even before his abdication the chambers of government and Napoleon's closest officials were telling him that it was time to stop fighting, and what resistance remained was pretty desultory.
Without resorting to the correspondence of individual Frenchmen, a pretty good metric for determining Napoleon's popularity on his return from Elba is this: by most accounts Napoleon had on the order of 50,000 troops ready to go when he re-assumed the throne in mid-March; by May he had on the order of 200,000 soldiers ready to go, with more getting prepped at army camps and depots. In the same vein, a fairly good metric for how the public felt about fighting was that it took the provisional government four days to ask him to leave Paris after the cards had fallen.
So how was it for any particular Frenchman? If you were a royalist, bad, if you were a Bonapartist, good, but in general your country has been ravaged by war and had its economy constrained by treaty. Regardless of how you happen to feel about Napoleon Bonaparte or the Bourbon Monarchy, it's hard to imagine feeling good about the state of the country.
Was there any chance of it being permanent? Britain/Prussia/Russia/Austria didn't take kindly to the return from Elba and immediately started military operations against France, but was it possible for Napoleon to hold it off?
Speculation and counter-factual argument are supposed to be bad history, but we can make some guesses based on the situation. It should be understood, however, that nobody can ever offer a definitive, correct answer to this question.
Napoleon's maneuvering up to the Battle of Waterloo had principally been focused on destroying the Coalition before it could properly mobilize, and failing that to defeat them in detail before they could link up with one another. By most reckonings, the entire Waterloo Campaign was essentially a gamble designed to produce that effect, and the fact that it failed suggests that his defeat meant that he had already tried his hand at the only strategy likely to succeed and been defeated. In a scenario where Napoleon lost Waterloo but didn't abdicate or surrender, no, that was probably it for our dear Emperor. He'd lost too many men, too much initiative, and too much popularity.
What if he'd won Waterloo? A lot of commentators are happy to lay the blame for the defeat at some frankly dimwitted mistakes made by his subordinates, though it's not at all clear that Napoleon's estimation of the situation with the Prussians was any clearer or more correct than that of Grouchy. That said, the battle was fairly closely fought, and it wouldn't have taken much in terms of being just a little more aware of von Blucher on the part of either Napoleon or his much maligned marshal to have turned the battle around. Well, the answer is that it's hard to know. If you assume that the casualties are similar to the historical battle, with only the outcome swapped, Napoleon has still lost a huge number of men to a foe that started out outnumbering him. If the casualties are different, then who knows? No matter what it looks pretty bad for Napoleon, though. France has suffered a huge number of casualties in the previous two decades of fighting, a lot of economic damage, and is opposed by almost all of the major powers of Europe. At that point the answer comes down to how much of a genius you think Napoleon is; maybe you're many historians, and Napoleon was a military mind beyond compare, or maybe you're B. Liddell Hart and Napoleon is superb at applying what he's learned, but adds little of his own.
So there's my not-a-straight answer: if you believe in Napoleon in your heart, he could have pulled it out. If you don't, he'd have been defeated.
Lastly, was the Hundred Days nothing more than a curious historical footnote in terms of effects? Did it cause anything to be really different than a universe where Napoleon never escaped Elba?
I'm inclined to say that it was more along the lines of, as you put it, "a curious historical footnote". The principal importance of the Wars of Revolution and Napoleonic Wars was two-fold: France, ostensibly the greatest power in Europe (not just ostensibly, really, given that they fought pretty much everyone for two decades before being defeated), was economically and demographically devastated; and the novel political ideas and structures that came out of the French Revolution and the rule of Napoleon were exported to almost the entirety of Europe. All of that had already happened by the time Napoleon departed for Elba, though. Napoleon and his revolutionary predecessors certainly changed the world, but they'd already done it before the Hundred Days.
Sources:
Tombs, Robert. France 1814-1914
https://www.worldcat.org/title/france-1814-1914/oclc/33281895&referer=brief_results
Furet, Francois. Revolutionary France, 1770-1880
https://www.worldcat.org/title/revolutionary-france-1770-1880/oclc/756698852&referer=brief_results
Chandler, David. Waterloo, the hundred days
https://www.worldcat.org/title/waterloo-the-hundred-days/oclc/6487634&referer=brief_results
Gildea, Robert. Children of the Revolution : the French, 1799-1914
Weber, Eugen. Peasants into Frenchmen : the modernization of rural France, 1870-1914
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Outside of Paris and the route Napoleon took, there was a good portion of France that was upset over the return of Napoleon. Troops stationed in Western and Southern France were harassed for being a part of the Hundred days as the locals wanted to return to the peaceful Royal days. It was so bad, Marshal Brune, stationed in Avegnion (will fix spelling), had be literally ripped apart when Napoleons defeat had reached them; the sad reasoning was because he was confused for Marshal Augereau, whom had participated in the repression of the Royalists in the early years of the Revolution.
The French government wasn't much changed betweem the Empire to the Monarchy, just the people in those positions. However, when the Hero returned, pro-Royalists fled while pro-Napoleon supporters had stayed and served with distinction.
As for the the big question, it goes into the realm of speculation. I wouldn't feel comfortable to say if the dream could have lived.
The after effect was terrible. The terms for surrender in 1814 had France restricted to her 1796 borders, allowing a little conquered ground to stay French. However, after Waterloo, it was pushed to 1789 borders and even worse reparations that hurt France more than anything else.