Alright so I think we need to tackle some misconceptions in your question before we get to Napoleon.

First off, in your title, you say that "one of the reasons why the French Revolution happened was to end the French Oligarchy". As with most things in history, it's a bit more complicated than that. I don't think most historians would feel comfortable agreeing with that statement, because there was not a sentiment at the beginning of the Revolution that anyone wished to 'end the oligarchy/aristocracy'. More than anything, what there was a push for was a more equitable financial burden. The nobility did not pay many of the taxes that was required of the commoners, and on top of that many peasants and landholders owed seigniorial dues to their noble landlord, as well as a hefty tithe to the Catholic Church. Pre-revolutionary France was an extremely complicated mixture of different taxes on different commodities that differed from province to province. What most Third Estate (i.e. non-noble or clerical) peoples of France called for before the Revolution was for the nobles to pay their fair share, and be taxed like the rest of the populace. There was absolutely not a popular call for abolishing the nobility outright, nor was there any calls to open up the government to the people (i.e. any insinuation that they wanted to abolish the monarchy).

Now on the other hand, there were many educated middle to upper middle class men who saw their progress halted because they were not of the nobility, and therefore entry to many of the governmental jobs was either blocked off to them, or the system of nepotism and favors dolled out to noble families meant that they were always superseded. These men, who absolutely comprised the Third Estate deputies in the Estates General, did believe the gov't needed to trend more towards a meritocracy than one based mostly upon privilege. However here again, these men were often most disgruntled at how poorly the aristocracy treated them, and wanted to be accepted by them, rather than calling outright for the abolition of the aristocracy.

Lastly there were the liberal nobles who thought that the monarchy shouldn't be so absolutist, and thought that a well-run France would be modeled after a Montesquieu-esqu structure where the nobility comprised a counterweight to the King. Here again though they were calling for perhaps a parliamentary-style chamber that could work with the King, but that would still include only a tiny portion of the kingdom's population in its body.

Just to put a fine point on it: even the most radical hardcore leftists did NOT go into the French Revolution (here I'm dating the beginning at the convening of the Estates General in 1789) calling for a Republic. Marat, Robespierre, Danton... all of these men are the embodiment of the hard-core left of the left, and yet all three of them believed in the monarchy and fully supported a more constitutional monarchy over the absolutist monarchy-- but none of them were calling for an abolition of an oligarchy, or the overthrow of the monarchy,

So why does that matter? Well I think this lays the groundwork for the heart of your question: Why did the French accept Napoleon? The French Revolution was at its core about a set of principles (liberty, equality, fraternity), modernizing and re-structuring a badly out-of-date kingdom, and putting into place a better government-- NOT solely about instituting a Republic. In fact Robespierre only tried to make a Republic work after the people had forcefully overthrown the monarchy on 10 August 1792-- he believed that it was too soon for a Republic, and that good citizens of a Republic needed time to mature into one.

I'm not sure if you're American like I am, but there is an interesting aspect to schooling in the US (and I'm sure many other democracies) that goes something like: Democracies are the best, everything else is despotism and sucks. Of course I'm being glib here, but it was a big wake-up call to me when I encountered Voltaire, the Enlightenment thinker, professing that he believed so-called 'Enlightened Despotism' was actually the best form of government. Guided by an enlightened ruler, this person would be able to impose his will (which would be what was best for the people) without having to deal with parties, factions, and self-interests. It's super fascinating and I could talk about it for hours, but if this interests you at all Aristotle elucidates on it brilliantly in his Politics. Anyway the most important takeaway here is that for the French who supported the Revolution, a successful Revolution didn't have to equal a Republic. What they really wanted was a better government that could do things about all of the issues that they had-- not a monarchy that was constantly in impotent gridlock as Louis XVI's was.

I want to touch briefly on another part of your question:
"how abusive the French oligarchy was which divided the upper classes from the lower classes and instigated the sheer massive anger of the French people when the French oligarchy started to make the lives of the French more difficult because of the increase in taxes"

I think you'd be better served here substituting monarchy for oligarchy, as that was truly the form of government, the important difference being a monarchy has a singular individual in sole control of the reigns, whereas an oligarchy is a small group at the helm.

>how abusive the French oligarchy was

Abusive doesn't really fit, and again I'm not sure if you're trying to say the monarchy was abusive, or the aristocracy. Certain aristocrats certain earned the ire of the lower classes whom they lived with, but others were beloved. The King also was generally beloved by his people, and though they despised the bad state of affairs in his government, they tended to blame his ministers and Queen for this.

>instigated the sheer massive anger of the French people when the French oligarchy started to make the lives of the French more difficult because of the increase in taxes

Again just to make sure we're on the same page, the monarchy collected taxes, not the aristocracy. France was in deep debt following a series of war efforts as you said, and the tax burden had more-or-less increased (though there were many efforts to gain revenue in other ways). The main ire as I mentioned above was that the nobility was not paying anything close to their fair share. There was a general seething resentment about this that was generally pushed over the edge in places where the lower classes also owned seigniorial dues to a local noble-- especially if that noble was not well loved otherwise. Watching people not pay their fair share of taxes plus having to pay them is what really raised the tensions between the the Third Estate and the Second Estate (nobles).