It should be no surprise to learn that Louis XVI's two younger brothers, Louis XVIII and Charles X, returned to the throne of France after the abdication of Napoleon. Not surprising, because the victorious allies, especially Russia and Austria, wished to reset the political map of Europe to pre 1789 and the French Revolution.
But you can only hold back the future for a certain amount of time. Louis XVIII was forced to accept a constitution and when his brother Charles X tried to row back on that meagre concession to The Revolution he was deposed in 1830. Further efforts to seed a constitutional monarchy in France gained some traction under Charles' cousin, Louis-Philippe.
Yet even the placid Louis-Philippe could not withstand the tensions within Europe in that Year of Revolutions of 1848. Forced to end his days in England, his regime was followed by the Second Republic headed by Napoleon's nephew, Louis Napoleon. In 1851 Louis Napoleon, through a coup d'état, became Emperor of the French as Napoleon III, thus emulating his uncle's career.
Napoleon III, outmanoeuvred by the wily politician Bismarck, saw his Army defeated in autumn 1870 at Sedan, after which he too found exile in England. With him the French monarchical tradition finally ended.
A Third Republic was now proclaimed in the aftermath of the Prussian/German defeat..................................
Further Reading
The Bourbons Kings of France Chs 7 & 8 Desmond Seward
Louis XVIII Philip Mansel
Citizen King TEB Howarth
History of Louis-Philippe John SC Abbott
The Shadow Emperor Alan Strauss-Schom
Napoleon III Fenton Bresler
The Franco-Prussian War Stephen Badsey