Grenouille's perfume acts like a love potion. He extracted concentrated pheromones from his victims, which make people fall in love. Of course the effect is exaggerated quite a bit, and it does not explain why women react to it, but it makes more sense than just 'people fall in love by smelling dead girls'.
In the film, unlike the book, the house of Msr. Baldini judders several times, foreshadowing its eventual collapse. During the second such time, we briefly see a look of confused worry steal over Grenouille's face. Obviously he took a quick sniff, estimated the level of decay that the building's foundations was on, and then carefully calculated his every move so that he would be out of the house before it fell.
At the end of the movie, the entire vial, enough to conquer the world through love, is emptied in Paris... the City of Romance.
As Brows Held High points out, Grenouille's execution would have been attended by whole families, and children as young as ten. That means, when the climatic orgy begins and everyone starts having sex with the nearest person, at least some people must have ended up screwing their relatives, a child, or both.