I think sexism is nearly as powerful against men than against women. The "man is strong/rich/tough/do man's stuff" and "women are sensible/sweet/dependent/do woman's stuff" cliché is still present. Well, in France, it is true. Perhaps less in Paris than elsewhere, but (and I don't live in Paris) it is quite present.
BUT
"Sexism" is heavier on women because today, we are more or less all forced to work, and live alone and find people to live with, etc.etc.
For men, it's easier to live in this because a man who -for example- is having a lot of partners is positively viewed. Not for women.
I do understand that a man can suffer from sexism if, for example, he considers that a woman has to earn less than him (even unconsciously) and that it is not the case. Perhaps it's nothing, but someday one of his friends, or at work, somebody will tell him, and he have unhappy thoughts. But most of the time it is NOT the case. And a man who would want to be a ballet or sewing will still be mocked. Not openly. But mocked.
It's like anti-white racism in white countries. It happens, but....but...much seldom.
However, for women it's a bit harder, because for many things we always have to prove that we are competent every time we meet someone, if you live out the boundaries. And nowadays, most women have to work, so apart from a few domains (social, care, health) the presence of women is not evident.
Try to go in a hardware store or discussing about computers (hardcore videogames such as DF ^^). A "boyish" woman can, perhaps.
I obviously like women stuff, but also very male things. If you try to be out of the invisible borders, you will be QUESTIONED. You are not where you are supposed to be. For people who have a strong personality, it won't be a problem. But for the weak, they will suffer, or they will give up. Men, as women.
Sexism is everywhere, even in us.