Why did it take so long to build the Arc de Triomphe?

Answer 1

Because it was Napoleon's idea, and th arch was still building when he fell from power. The restored Boubon monarchy had no intention of finishing a monument to a usurper, so it was not for some time that work restarted. I repeat here my fuller answer to a similar question yesterday:

In 1806 Napoleon asked the architect Chalgrin to construct a gigantic triumphal arch in honour of the French Army. The top of the Chaillot hill had to be levelled, and the foundations gave some difficulty, so that by the time the new Empress Marie-Louise arrived in 1810, the arch was only a few feet high. As the Emperor insisted that his bride must drive into Paris through this new gateway, Chalgrin had to get friends from the Theatres of Paris to construct a fake arch of wood and canvas for the occasion. When Napoleon was defeated and exiled in 1814, work stopped, not to be started again till Louis-Philippe ordered it in 1832. It was finished in 1836.

Answer 2

The US Civil War intervened, delaying the availability of materials and workmen.

(see related link)

Answer 3

Construction was initially halted because the private organization funding the monument ran out of money. Construction was completed decades later when the government started paying for it.