gen2 is correct in all that he says.
Benzene is indeed a very toxic, carcininogenic chemical and in my laboratories, severe safeguards have to be in place before the top of the container is opened. When we need it from the stores, it's transported on special trolleys that make spillage virtually impossible.
Nevertheless, benzene is detectable in perfumes in minute amounts. When it is there, it's usually as a result of degradation or impurities in the substance in the perfume that makes it smell nice.
As an example, there's a chemical called 4-hydroxy-3-methoxybenzaldehyde which is derived from benzene. This substance is more commonly known as Vanillin and it adds a vanilla like odour to perfumes. Now you may think that such a complex chemical would have to manufactured in the laboratory, but nothing's further from the truth. Vanillin occurs in nature in vanilla pods as well.
Now if you look up the structural formula of vanillin on Wikipedia etc, you'll see it's basically a hexagon with a number of "arms" leading off it. The hexagon is known as a benzene ring and is a simple way for chemists to represent C6H6, also known as benzene.
So what's so special about this benzene ring? Well, it's the fundamental basis for something called aromatic organic chemistry and it's found in all aromatic organic compounds. But here's the important part. The benzene ring is not "free" to impart its toxic properties within vanillin, but locked safely away.
In general, all organic compounds including the synthetic chemicals used in perfumes are manufactured by adding, removing or relocating the functional groups shown at the end of those arms shown in the Wikipedia article. Benzene based odours must not be thought of as extracted but as derived from the repositioning, adding or subtracting of the functional groups. Some of the changes that occur as a result may be very subtle and hardly