We document the individualization of wealth in France between 1998 and 2015, using precise survey data on the property titles of assets. It is characterized by an increase in the share of wealth which is individualized by spouses (vs. jointly owned) and by an increase in the share of wealth held by singles. We show that the usual measures of wealth inequality, which allocate the same share of household wealth to each spouse or partner, overestimate the share of wealth held by women. This results in an underestimation of both the level and the growth of a) wealth inequality between individuals and b) the gender wealth gap. We argue for better consideration of the ownership status and intra-household distribution of wealth in the measurement of wealth inequality.