The hardest thing is deciding the victory scenario. Every victory scenario would result in key points being different. I'm going to base my text on the idea of the French not managing to have the Peninsula quagmire, still being involved in the War of the Fifth Coalition to beat Austria, but maintaining a detente with the Russians long enough that the British ultimately come to the peace table in response to growing French naval strength (which was historically expanding at a rapid pace before the final defeat), the seeming futility of the war, and financial woes, resulting in a largely utis posseditis peace settlement.
In my opinion it would probably be more peaceful and prosperous in the long term, split into its blocs of the Russians, French, and British: none of them would be, after the solidification of the empire, capable of wiping the others out without a long and bloody war, although inherently the British are the most vulnerable: Britain's only card is its navy, and if it ever came to be the case that the French gained an advantage over it, then the lack of strategic depth, ground forces, and size could easily make that fatal. It might be wishful thinking on my part, but I think the trio structure and the power of each individual combatant might be enough to prevent another war, as compared to the larger allotment of smaller great powers which existed historically.
Economically speaking I have a rather optimistic view of the Napoleonic empire. In the Rhineland at least, businessmen were among the most important pillars of the regime, and it did see important growths in industry, textiles in the north being one that I particularly remember (therein helped by the Continental System which removed English economic competition), and Napoleon was quite interested in various infrastructure projects. The size of the market of the Empire is huge. I presume some form of economic protectionism against English imports would continue, which would make much of Europe much more resistant to English imports. I'd expect the Continental System to be modified, presumably to become much less stringent, but still being used. Economic development across Europe I would expect to be roughly the same, higher military expenditures and their drag upon the economy being balanced out with the large integrated market and vigorous colonial expansion, and perhaps higher in some of the more backwards and reactionary regions that are hit by French attempts at "rationalization" and the like. Russia I think would follow essentially the same course as historically, unless if it was impacted by much more liberal reforms than happened historically.
Britain, if I may go out on a limb, I think would be economically much more lackluster than historically, denied markets and opportunities to invest across Europe, and as I elaborate on later, a potentially more muddled market in Latin America. The existence of the French Empire would mean that there would be a need for constantly higher military expenditures, and that is the other dangerous thing: the British had an extremely high debt load from the Napoleonic wars. Historically it wasn't a serious problem, but presupposing lower growth with more vigorous international competition and reduced export markets, and a constantly higher military burden, the negative effects would reinforce each other and it would be much harder to finance debt service and it would impair the British economy. Not enough to cripple it in any way, but as a drag upon their efficiency.
Colonial wise, Napoleon certainly was very interested in colonial expansion. As noted in the paper Napoleon and the Universal Monarchy:
Also in 1808, Napoleon sent an exploratory party to Algeria in preparation
for a possible invasion. Once the invasion of Spain took place,
Napoleon intended to assume control over all of Spain’s colonial possessions
in the New World. He sent secret agents to the Americas to stir up
rebellions against Spain, offered financial and military assistance to the
rebels, and even planned to recognize the independence of Venezuela in
1812.70 Plans were also vaguely considered to invade Brazil, Havana,
Mexico, the Philippines and even the Dutch East Indies, but he never
explicitly stated in writing why he wanted to send troops to those countries.
71 It has to be assumed that it was intended as an attempt to foil
Britain’s trade and to dominate the world’s colonial markets.
Frankly quite a number of these to me seem like they would fail, particularly the ones in the New World, the closest I can see to success there is the French backing up the Spanish Bonapartists in reclaiming the colonial empire and effectively being the real ones to control it: even that I find doubtful, as the degree of institutional damage inflicted upon the Spanish colonial empire by this point in my opinion renders it un-salvageable to take it all back. Venezuela and Chile both to my understanding however, saw effective Spanish resistance, so with French support it might not be impossible for certain key zones to be retaken. They would probably have to deal with British support for the rebels however - according to Expansion mondiale et dépendence occidentale the British even historically provided arms to anti-Spanish rebels from my recollection, and that would be magnified to a huge degree here. But projects like going to East Asia, or conquests in North Africa, are entirely feasible. I'd expect overall a significant acceleration of European colonialism early in the 19th century, driven by Napoleon's interests in colonialism leading to a more vigorous Anglo-French colonial rivalry, with French efforts in places like North Africa being matched by more rapid British expansion in India.
As far as French as a language, the story is a complex one. The French were interested in making French the high language throughout the newly French regions annexed to the empire, Italy, Belgium, the Rhineland, etc. I would recommend reading The Language Question under Napoleon for additional details, but broadly the results were a mixed bag and generally pessimistic, and there wasn't a real success for making the regional elites francophone: there wasn't any violent armed resistance either (after all, it was principally targeted to elites), but rival high languages continued to be, well, rivals, and the French had to constantly accept that and put off their plans for implementing French into those new regions. I do expect a Frenchification over time, but it would be a relatively slow and gradual one, fraught with problems, and one principally among the elites. At the same time the views of mass uprisings are ones which I generally think are overrated: under Napoleon (as opposed to the chaotic periods of the 1st Republic), the French didn't have any serious rebellions in their 1797 borders. Rhenish identity has always been noted for its bridge effect between Germany and France, Belgium I think can be reasonably well assimilated into France in the long run, and ditto for the parts of Italy that the French directly control.
Internally in France, I think that things might be smoother in regards to patois, since the Church post-Restoration was engaged in a re-Christianization campaign, and it identified patois as being an antidote to the liberal and modern values which it viewed as destroying French Christianity. Without the Bourbons being restored, I'm doubtful about the idea of the same Christian revitalization project happening, so patois doesn't seem like it would become quite the cultural clash that it did - and even historically, the supposedly brutal effects of the Third Republic's gaullicization is somewhat exaggerated.
Externally, while agreeing that France's role as the international lingua franca and prestige language will be both confirmed and reinforced, in the short term I expect that the Napoleonic project might actually reinforce multilingualism. Napoleonic lycées and higher education was not simply French - it was the expression of a broader, European and Classical civilization, and so Latin was still something which commanded tremendous prestige and utility, and in general bilingualism was a highly useful trait in the newly annexed regions. The Napoleonic army, which I presume will have plenty of postings abroad, both in colonial expeditions, and across Central Europe, was never really a tool for imposing French, and conversely it was very much a multilingual project, which promoted education in other languages as part of communication, both internally due to having plenty of "national" units speaking other tongues, and externally, to talk to the population. A Europe which is more interconnected, even with the promotion and increased prestige of French, will see more multilingualism. I don't disagree with the comparison of places like Sofia to Antwerp, just it won't be the complete picture in my opinion.
Which brings up another point, concerning borders. The French annexed the Netherlands and Northern Germany, ostensibly at least to deal with the threat of smuggling. Imo I think Napoleon would be smart enough to realize that after the war that's quite foolish and put them back on their normal basis, maybe with some reorganizations in Northern Germany in rationalizing it.
Speaking of Russia, this would have major implications for them as well -- while the effects of averting the Invasion of the Grande Armee on Russian domestic policy alone is worth a discussion, we can, for the purposes of this thread, turn the focus on her war with the Turks (which started in 1806). The bottom line there being that, with a much freer hand the OTL, Russia stands a very good chance of wiping out Ottoman dominance of the Balkans far sooner than OTL, which would have further knockoff effects on the remaining Ottoman Empire as a whole.
To note upon the Ottomans, the French were historically quite concerned about their break up and scrambling to get the pieces if that happened. In 1808? (I probably have gotten the year wrong), the French had a chance to invade Sicily with the concentration of some naval assets to hit it - it wasn't necessarily an inevitable plan, and it could have gone south easily enough, but it did have a good shot of succeeding. Instead, they diverted their naval assets to escort supply ships to reinforce Corfu, apparently under the belief that the Ottoman Empire would fall apart soon and they had to ready to get their piece of the pie. I don't know how effective the French would have been, but any split of the Ottoman Empire is likely to be very much a scramble, as the British, French, Russians, and various minor factions try to get their pound of flesh.
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Politically I think all three regimes are tough enough to ride out internal disturbances and unrest, and that it is unlikely that any of them would be easily overturned by revolution, although maybe reformism will be important in Russia as others have noted. The Napoleonic regime is reformist and egalitarian enough to be able to keep the lid on most of its internal issues, and nationalist revolts don't seem like they could really destroy it, given the solid French core. States in its zone of influence, like the Austrian Empire, might have more problems, but even there they survived historically. The British I think would have a rougher time of it, with a worse economy as I hypothesize, but ultimately they can make conceptions to the masses if needed to prevent revolution: there is plenty of ground to give for elites to the masses.
Overall it seems like a world which would be more "even", with some mild depression on the part of Britain, and a more diffused layout of commercial power and changes around Europe, faster colonialism, and being more similar to the 18th century historically in terms of centers of cultural production and diffusion.