  The aim of this paper is to show the existence and give an explicit
description of a pseudo-Riemannian metric and a symplectic form on the
$\mathrm{S}\mathrm{L}(3,\mathbb{R})$-Hitchin component, both compatible with
Labourie and Loftin's complex structure. In particular, they give rise to a
mapping class group invariant pseudo-K\"ahler structure on a neighborhood of
the Fuchsian locus, which restricts to a multiple of the Weil-Petersson metric
on Teichm\"uller space. By comparing our symplectic form with Goldman's
$\boldsymbol{\omega}_G$, we prove that the pair $(\boldsymbol{\omega}_G,
\mathbf{I})$ cannot define a K\"ahler structure on the Hitchin component.
