I was randomly reading WWII history articles, and came across an interesting anecdote that the governor, Dietrich Choltitz refused the order because he loved French culture, but it was later alleged that he would have been incapable of carrying out the order due to the rapidly disintegrating military situation.
What was the situation like in Paris when the order came in, and do we know if it was given any serious consideration/preparation?
Hitler's order of 23 August was quite clear: "Paris darf nicht oder nur als Trümmerfeld in die Hand des Feindes fallen" — Paris must not, other than as a field of ruins, fall into the hands of the Allies." This certainly led to the arrangement of mines and other demolition efforts on bridges and major monuments around the city. Many now believe the Cholitz eventually refused the command in order to save his own hide and his family, rather than some deep-seeded love of the city and its inhabitants. He wrote a memoir in 1951 and the event has been dramatized numerous times since. Cholitz was certainly not a man known to disobey orders lightly, and there are uncorroborated reports that he was secretly recorded in captivity in London as admitting that the most difficult order he ever carried out was the extermination of Jews.
On a technical level, even with Allied forces bearing down on the suburbs on the same day as Hitler's order, the Germans were more than capable of destroying the Eiffel Tower and many other landmarks around the city. In fact, the Germans had become the world experts on the deliberate destruction of cities' infrastructure and monuments. They so thoroughly destroyed the ports of Normandy that the Allies would not have them even partially operational by the end of the war. The Germans had practiced this trade in North Africa first, then in Italy. They absolutely wrecked the infrastructure of Naples before withdrawing in late September 1943.
In both the case of Naples and of Paris, organized and determined local resistance by the city inhabitants surely dampened efforts to carry out Hitler's orders (Naples was similarly ordered to burn). Naples had its famous quattro giornate di Napoli and the French too made life so difficult for the Germans in the last days of Paris occupation that destruction of non-strategic structures was probably very far down their list of concerns. Strategic targets, however, like power generation stations, waterworks, and bridges, seldom escaped their capable ministrations.