  In 2008 or earlier, Michel Mend\`es France asked for an instance of a real
number $x$ such that both $x$ and $1/x$ are simply normal to a given integer
base $b$. We give a positive answer to this question by constructing a number
$x$ such that both $x$ and its reciprocal $1/x$ are continued fraction normal
as well as normal to all integer bases greater than or equal to $2$. Moreover,
$x$ and $1/x$ are both computable.
