1900-1905: Final assembly of a caisson to be buried in the place St-Michel
1900-1910: Digging a trench in the avenue de l'Opéra
That this was possible was due to the work of Georges-Eugène Haussmann who, under a commission by Napoleon III, created a new Paris with wide tree-lined boulevards and extensive gardens which replaced the narrow twisting streets of the old Paris. Thus, much of the Métro could simply run in straight lines down the centre of the wide roads. But of course this meant that for years Paris was a building site. From these two photos you can get an idea of how awful this must have been for the residents.
Better still, open this PowerPoint file which has more photos of Paris with the work going on. You don't have to click through all 85 of them, but they are worth a look. And if you have your loudspeakers switched on you will hear Le Trou de Mon Quai, "une p'tite chansonnette métropolitaine", a manic but charming ditty written and recorded in 1906 by someone called Dranem who cackles away as if he was having a really good time amid all the suffering of his fellow-citizens.
Thanks to Thierry Fournier for the link