Learn French: Le héros vit le parchemin sacré et eut peur. - The hero saw the sacred parchment and was afraid.

It can! In the present tense, il vit means "he lives" (from the verb vivre). But in this literary past tense (the passé simple), vit is the "he/she/it" form of voir (to see). Context is your best friend here: heroes usually see sacred parchments rather than living them.

What verb is eut? It looks really strange!

Eut is the passé simple form of avoir (to have) for "he/she/it". In spoken everyday French, you would hear the passé composé (a eu) or the imparfait (avait) instead. You will see eut very frequently in novels and fairy tales.

Why does it use eut peur instead of a past tense form of "to be"?

In French, you "have" fear rather than "being" afraid. The core expression is avoir peur (to have fear). Since the story is written in the passé simple, the verb avoir becomes eut, so eut peur literally translates to "had fear".

Why is it le héros and not l'héros?

The word héros starts with an "aspirated h" (h aspiré). Even though you don't pronounce the "h", it acts like a solid consonant barrier. This prevents you from dropping the "e" in le (elision) and also blocks any connected pronunciation (liaison) from preceding words.