Applying a function to a nested list

Replace[l, x_List :> F[x], All]

F[{F[{F[{a, b}], c}], d}]

Also

ClearAll[f]
f[Except[_List, x_]] := x;
MapAll[f, l]

f[{f[{f[{a, b}], c}], d}]

Another possibility, if you want just lists to acquire the F wrapper:

l /. List -> F@*List

F[{F[{F[{a, b}], c}], d}]

F@*Reverse@Map[F@*Reverse, l, -2]

F[{d, F[{c, F[{b, a}]}]}]

Fold[F[{#2, #1}] &, Flatten[l]]

F[{d, F[{c, F[{b, a}]}]}]

Related