Exil is usually imposed, though CNRTL's own entry allows a fixed term as well as a life sentence and a voluntary departure too; dépaysement is usually temporary and often chosen. But the distinction is younger than it looks — CNRTL notes the oldest sense of dépaysement was quasi-synonymous with exile. The pleasantness is a later acquisition.
Side by side
Aspect
Dépaysement
Exil
Chosen
Usually
Usually not
Duration
Temporary
Usually permanent — CNRTL also allows a fixed term
Valence
Either
Painful
Originally
Near-synonyms
Near-synonyms
What each one means
Dépaysement
Dépaysement is a change of surroundings and habits — usually the pleasant kind you travel for, sometimes the disorientation of being lifted out of your familiar setting. In French law it also means moving a trial to another jurisdiction.