There is no "best word". Good translations depend on the context.

Possible ones for "he fled" might be:

Il s’est échappé (de sa cellule, de son enclos)

Il s’est évadé (de prison)

Il a fui (ses responsabilités, son pays, sa famille, à l’étranger,…)

Il s’est enfui (de chez lui, de son pays, à l’étranger,…)

Il a quitté (son pays/sa femme/…)

They are quite similar in meaning with a difference of emphasis,

• fuir put the emphasis on what is fled from (even if it is implied).

• s’enfuir put the emphasis on the movement itself.

And to complete with the other verbs cited by @jlliagre:

• s’échapper implies that there was a constraint.

• s’évader implies a stronger constraint, probably legal, the most common usage is for convicts and prisonners.