Actually, that's only the OFFICIAL truth (or an architect fantasm), as much as saying that limiting the number and speed of cars on the Peripherique will make better living conditions for those living there...
Truth is: the Peripherique is largely more used by the suburbs (even to go from one to the other, east and north to west and south mostly) than by Parisians. The plans on the Peripherique will mostly impact badly these people on their day-to-day but... the Mayor Hidalgo think that
1) it will help her to be reelected by the "bo-bo" (bourgeois boheme - left upper class) living in Paris (that has been too costly for other population)
2) it will leave a "testament" of her Mayorship "in the stone" (a bit like Mitterand did with Palais du Louvres, Arche de la Defense and so...) and turn Paris into a tourist dream (like Venice) more than an economic and social capital