  We show that any co-orientable foliation of dimension two on a closed
orientable $3$-manifold with continuous tangent plane field can be
$C^0$-approximated by both positive and negative contact structures unless all
the leaves are simply connected. As applications we deduce that the existence
of a taut $C^0$-foliation implies the existence of universally tight contact
structures in the same homotopy class of plane fields and that a closed
$3$-manifold that admits a taut $C^0$-foliation of codimension-1 is not an
$L$-space in the sense of Heegaard-Floer homology.
