Learned fool has a fair number of Ngram hits.
PRINCESS
None are so surely caught, when they are catch'd,
As wit turn'd fool: folly, in wisdom hatch'd,
Hath wisdom's warrant and the help of school
And wit's own grace to grace a learned fool.
- Shakespeare, Love's Labours Lost | Act 5, Scene 2
A rarely used French/Greek import:
morosoph (Noun) (obsolete) A philosophical or learned fool.
Urquhart translated Rabelais, and for morosophe, came up with morosoph. Perhaps the only usage in English, (last sentence):
He says you are a fool. And what kind of fool? A mad fool, who in your old age would enslave yourself to the bondage of matrimony, and shut your pleasures up within a wedlock whose key some ruffian carries in his codpiece. He says furthermore, Beware of the monk. Upon mine honour, it gives me in my mind that you will be cuckolded by a monk. Nay, I will engage mine honour, which is the most precious pawn I could have in my possession although I were sole and peaceable dominator over all Europe, Asia, and Africa, that, if you marry, you will surely be one of the horned brotherhood of Vulcan. Hereby may you perceive how much I do attribute to the wise foolery of our morosophmorosoph Triboulet.
-- Gargantua and Pantagruel, Book 3, Chapter XLVI