Is there an "invisible tax" on women's consumer goods?

The French finance ministry is to investigate claims that women typically pay more than men for similar consumer goods, like shampoos, deodorants, razors and other goods marketed as "feminine". Does it constitute an "invisible tax" on women?

That group is called the Georgette Sand Collective.

Sophie Janinet works there, and I put it to her that some of these products, like razors, could be cheaper for men... simply because they buy more of them: