  A $2$-distance $k$-coloring of a graph is a proper $k$-coloring of the
vertices where vertices at distance at most 2 cannot share the same color. We
prove the existence of a $2$-distance ($\Delta+2$)-coloring for graphs with
maximum average degree less than $\frac{8}{3}$ (resp. $\frac{14}{5}$) and
maximum degree $\Delta\geq 6$ (resp. $\Delta\geq 10$). As a corollary, every
planar graph with girth at least $8$ (resp. $7$) and maximum degree $\Delta\geq
6$ (resp. $\Delta\geq 10$) admits a $2$-distance $(\Delta+2)$-coloring.
