How justified is the claim that Napoleon I constructed a new order by borrowing from both the ancient regime and the revolution?
This claim would be hard to justify. Napoleon borrowed little from the ancien regime other than the re-establishment of the Catholic Church. Even so, the Concordat which he signed with Pope Pius VII gave him the right to nominate bishops and pay clergy. The Revolution had attempted to remove the influence of the church entirely. He did guarantee equality before the law as under the Revolutionary governments, and the security of wealth and property.
Under Napoleon, women lost nearly all the rights they had gained under the Revolution. They lost the right to contract or have bank accounts in their own names, and the father was established as absolute ruler of his household. Free speech and freedom of the press were virtually abolished, and the number of newspapers was reduced to four; they were primarily papers which would glorify Napoleon.