In ${XeF}_2$, two bonding and three non-bonding electron pairs are present, i.e., xenon atom undergoes $s p^3 d$ hybridization.
Trigonal bipyramid configuration comes into existence. Non-bonding electron pairs always occupy the equatorial positions and thus, fluorine atoms occupy the axial positions.
Hence, ${F}-{Xe}-{F}$ molecule is linear.