  Let $G$ be a real reductive algebraic group with maximal compact subgroup
$K$, and let $F_r$ be a rank $r$ free group. We show that the space of closed
orbits in $\mathrm{Hom}(F_r,G)/G$ admits a strong deformation retraction to the
orbit space $\mathrm{Hom}(F_r,K)/K$. In particular, all such spaces have the
same homotopy type. We compute the Poincar\'e polynomials of these spaces for
some low rank groups $G$, such as $\mathrm{Sp}(4,\mathbb{R})$ and
$\mathrm{U}(2,2)$. We also compare these real moduli spaces to the real points
of the corresponding complex moduli spaces, and describe the geometry of many
examples.
