How justified is the claim that Napoleon constructed a new order by borrowing from both the ancient regime and Revolution?
The question seems to be referring to the idea that Napoleon kept a number of French Revolutionary reforms, especially those that tended to empower the French state, while essentially reestablishing a hereditary monarchy, which was, of course, what the radical phase of the Revolution was aimed at destroying.
His law code, the famous Code Napoleon, is one example: It provided equality of all men before the law and protected private property, two major goals of French liberals during the early days of the Revolution. He also valued education highly, and created a bureaucracy where middle-class Frenchmen could rise on merit more than family ties, as in the old regime.
But Napoleon also invited many exiled nobles back, giving them key officerships in the army, rolled back women's legal rights in the Napoleonic Code, and crushed free speech and free press. Some people might say this was also not inconsistent with the Revolution, especially under Robespierre, but basically France became a police state, just as it was to a great extent under the Bourbons. He also made peace with the Catholic Church, which had been alienated by the Revolutionaries. And of course, while he began as a so-called "First Consul," he eventually had himself crowned Emperor of the French, and designated his family as heirs.
Basically, Napoleon was really successful at harnessing the nationalistic sentiments let loose by the Revolution, compromising with the middle classes, instituting a number of reforms that he probably sincerely believed in, and restricting civil liberties, all of which were aimed at creating a France that would be capable of conquering all of Europe.