Well, France's demographic transition started earlier - around 1790 or 1800 - so 1815 is kind of a bad date for it (in particular, it wasn't because of Nappy or anything like that).
But let's say it hadn't happened. I'm not exactly sure what it would involve, because it happened so atypically early in France's development. Let's ignore the AHC part and just do a WI. In the ATL, France's demographic evolution is similar to that of Sweden - I'm picking Sweden and not Germany because its borders have been more stable, and its late-18c/early-19c statistics are the most reliable. This means France has 27.5 million people in present-day borders in 1800, loses the Napoleonic Wars on schedule because all of Europe ganged up on it, and then undergoes fast population growth. There's still resentment over the monarchy, so the 1830 and 1848 revolutions occur on schedule, and Nappy III still wins.
Fast forward to 1870. France has 49 million people (OTL: 37 million), Germany has 41 million. Germany is only starting to industrialize, so tech levels are comparable. France still has a Paris-centered railway network, but the population boost gives it a somewhat thicker network, with better connections between the Southwest and Provence, and a denser network in Nord and Alsace. It has an easier time moving troops to the front, and more manpower; the German attack stalls, and after a protracted war of 2 years, France repels the Prussian invaders. Germany unifies anyway, to balance against France, but the reparation payments France imposes on Germany to pay for the carnage caused in Alsace and Lorraine lead to a lot of bitterness among the secondary states, which blame Prussia for dragging them to war and saddling them with debt.
In the following 20 years, Germany is rife with instability. Austria-Hungary is trying to peel off German states to weaken Prussia, Bavaria and Baden are openly calling for making the emperor's position elective, and a socialist commune launched an uprising in Hamburg in 1882 that was only suppressed after three weeks and a few thousand dead. The instability spreads to Austria-Hungary, and liberal nationalists are calling for the dissolution of both Prussia and A-H and their replacement with a federal German republic. Germany's only ally is Belgium's conservative and Flemish factions, since both France and liberal Walloons call for French annexation of Belgium; Belgium's population grows at the same rate as France's starting after the Napoleonic Wars, and by 1900 it has 8.5 million people (OTL: 6.7), and France has 60 (OTL: 39). The Second French Empire remains stable, and has an easy time suppressing worker revolts; Nappy III dies in 1881 and is peacefully succeeded by his son Nappy IV (1842-1926, r. 1881-1926).
In the Scramble for Africa, France explicitly challenges British domination of the world. A brief colonial war in India ends in a French defeat, but in Africa, France manages to take control of the Congo, West Africa (except Nigeria and the Gold Coast), and parts of East Africa. France engages in naval buildup with Britain, and by 1900 its navy is only 20% smaller than Britain's, while its army is much larger.
In 1901, expeditions from Britain heading south from Kenya and from France heading west from Dar es Salaam meet around Arusha and begin a skirmish: France is attempting to connect Africa west-to-east, from Napoleonville on the Congo to Dar es Salaam, and Britain is attempting to connect it north-to-south, from Cairo to Cape Town. It is later called the Great Skirmish, due to its far-reaching effects combined with the limited death toll. It is agreed that Britain will get sole control of East Africa and France will vacate Pondicherry, but in exchange, Thailand is in the French sphere of influence, and Britain will remove its objection to France's annexation of Belgium. In 1903, 52% of the eligible voters in Belgium agree to French annexation in a referendum, including 70% in Wallonia and Brussels but only 33% in Flanders; while the election was technically free, Flemings with poor French language skills in many cases could not find the polling places, especially in Brussels. France immediately moves in, and begins a campaign to suppress the Dutch language, which it considers a sign of hostility.
By this point, the Netherlands has already established consociationalism, and nationalist Catholic elements indicate that they'd be open to annexation of Flanders. To protect itself from French aggression, it allies with Britain, as does Germany. While stability is restored for now, the Netherlands and Germany grow increasingly dependent on Britain. So far, all European countries are as rich as in OTL, except Germany, which is poorer because of the instability between 1870 and 1890 and the lack of captive colonial export markets.
With the Scramble for Africa complete, the colonial powers turn to China. They reject the US's proposal for an open door policy, and carve China: Japan gets Taiwan and Manchuria, Britain gets Shanghai and points west, France gets Guangdong and Fujian and points west, the US gets Beijing and the North China Plain south to about the Huai. This division is hammered out in 1904 and is complete by 1920.
The apparent stability masks deep contradictions, especially in France, which has the highest inequality among major countries. Only Paris, Brussels, and Wallonia are as rich as Britain; the rest of France is poorer, and begins to sour on Nappy, who it supported against the wishes of the Parisians up until now.
In 1918, the Poles revolt in eastern Germany, with Russia's support. Germany immediately puts down the revolt, massacres the Polish intelligentsia, and when Russia objects, it invade, annexing most of OTL's Poland's interwar boundaries, except the East Slavic far east. It immediately begins to dump settlers in the region, from all states rather than just Prussia, to mollify opposition from various local notables.
In 1920, taking a cue from the Poles, the Czechs rise up, proclaiming a Czechoslovak republic in all of Bohemia, Slovakia, and Galicia. A-H spends a year trying to put down the rebellion before withdrawing; subsequently, the Sudeten Germans maintain resistance and call for reintegration into Austria, launching an intermittent guerrilla campaign, but in most of the boundaries of the new country there is quiet. This creates a chain reaction, destroying A-H by 1924, leaving a rump Austria, undecided whether to join Germany or remain independent.
Arab intellectuals in Paris and London watch the dissolution of A-H with glee, and with France and Britain's support go back to the Middle East and launch revolts against the Ottoman Empire. Zionism manages to survive with Britain and France's support - France especially views it as a convenient way to get rid of its Jewish population. German intellectuals at this point proclaim that Germany is being bypassed by Britain and France, which are dividing the world between them. A second Polish revolt in January of 1926 leads to a cascade of revolutions, creating a new Polish republic as well as republican regimes in Yugoslavia and Austria. By April this leads to the fall of the Hohenzollerns, and a brief civil war in Germany, in which liberals proclaim a federal republic, including Austria, but face guerrilla warfare in mixed Polish-German areas, outright rebellion in Franconia and rural East Elbia, and strikes and industrial sabotage in the Ruhr. When Nappy IV dies in August, his unpopular son is prevented from taking the throne, and French urbanites, by now 55% of the population, declare a Third Republic, with universal (not universal-male) suffrage.