What happens if Napoleon dies in January, 1815? Say he catches something whilst in exile, or simply dies from a disease? Naturally this means no 100 days, does this strengthen the Bourbon hold on France, does it shift Bonpartist sympathies to his son, or to his nephews?
France is in a much better shape. It can retain the 1792 borders (so including Savoy), it doesn't have to pay for the allied occupation, it is in a much stronger position in the Congress of Vienna. Maybe Talleyrand can strengthen the French diplomatic position against Great Britain or Austria?
Regarding French domoestic politics, there will be no White Terror (essentially the royalist reaction at the end of the Hundred Days). The royalist position will be weaker, liberals like Constant and revolutionaries like Fouché will continue to play an important role. The régicides like Cambacérès, Sieyès or Fouché will not have to leave the country.
Bonapartism will be very different to OTL's movement. The army was very dissatisfied with the diminishment of the number of regiments (necessary after the end of the Napoleonic Wars), and we might see some conspiracies or coup attempts - but nothing serious (think of the two amateurish attempts Napoleon III made in 1836 and 1840; both were unsuccessful).
At the same time, Bonapartism will lack the experience of the Cent Jours. While from a European perspective, the Hundred Days were a French defeat, Napoleon considered them as a personal victory. He had used the Hundred Days to forge his image as a popular hero, supporter of Liberalism; his captivity on St. Helena made him the idol of Romanticism, and Las Cases' Memorial of Saint Helena depicted him as the liberator of oppressed nations and friend of progress.
I doubt that Bonapartism will gain so much sympathies without the ultimate battle at Waterloo and the exile on St. Helena.
Another interesting region will be Italy, since the Congress of Vienna maintained Joachim Murat as King of Naples. Murat was somewhat a progressive and mondernized his kingdom - in OTL he attempted to unite Italy in 1815, which can be described as a first Risorgimento. I don't think that he would have attacked the Austrians without the Hundred Days, but Naples might well become the strongest state of Italy and unite Italy under the dynasty Bonaparte.
Alright interesting, would be interesting to see if Republicanism could be defeated as an ideology.
Why should it be defeated...? The 19th century was a century of rationalism. Hereditary monarchy wasn't adapted to the spirit of the era: why should a person hold a public office just because his father hold the same office?