That the restoration of the Bourbons was a re-enactment of the Restoration of the Stewarts was not only a widespread belief at the time, but one that was, in itself, an important historical fact. If the French Restoration went the way of the English, it was partly because it was expected to do so.
The parallel was formally close: Louis XVI and Charles I; Napoleon and Cromwell; Charles X and James II; Louis-Philippe and William III. All went roughly according to the historical plan, except that, in England, there was no 1848, no Second Republic, no Second Empire—which underlines the truth that not every country that needs Whigs gets them