Affirming Andrew Leach's answer, the Paschal Greeting can be classified as a set phrase in many languages--especially those influenced by Orthodox Christianity.

He is risen is perceived in modern English as a predicate adjective, but it is technically an archaic present perfect construction from Matthew 28:6:

He is not here: for he is risen, as he said. Come, see the place where the Lord lay.

KJV Bible Gateway

Emphasis mine

The translators of the KJV used this construction to translate the aorist passive ἠγέρθη in the Greek text:

οὐκ ἔστιν ὧδε, ἠγέρθη γὰρ καθὼς εἶπεν: δεῦτε ἴδετε τὸν τόπον ὅπου ἔκειτο:

qbible.com

Emphasis mine

The Greek aorist passive has no precise equivalent in English, and this present perfect construction was particularly useful for verbs that presented an ongoing state resulting from a past action like ἐγείρω:

A. to arouse from sleep, to awake

B. to arouse from the sleep of death, to recall the dead to life

blueletterbible.org

Some have tried to parse this as a simple present passive construction, but that is problematic. To distinguish it from the predicate adjective with a past participle, the simple present passive normally demands an explicit agent :

Simple Present

Active : Once a week, Tom cleans the house.

Passive: Once a week, the house is cleaned by Tom.

englishpage.com

Emphasis mine

Regardless of the parsing, the expression is designed to emphasize--for theological reasons--the present state of a past action. Orthodox Christians are taught the preeminence of the historical resurrection of Jesus Christ as the foundation of his ultimate sovereignty and their eternal hope, impregnating the entire antiphonal greeting with theological significance:

Christ is risen!

He is risen indeed!

Alleluia!

Unbelievers can find solace in the fact that this greeting is rarely used outside of the church building.