Is there a "Church Approved" alternative text for the Hail Mary?

One alternative might be the eastern rite hymn Rejoice, O Virgin Theotokos.

I know, it doesn't sound like a version of the Hail Mary but the Church Slavonic rendition is prayed at the small beads on the rosary in the byzantine rite.

Here's an English rendition which has one less verse than the above cited Church Slavonic version:

O Godbearer Virgin Mother now rejoice!
Holy Mary full of grace, the Lord is with you.
Blessed are you among women and blessed
is the fruit of your womb, for you have borne
Christ the Savior, the Deliverer of our souls.

You can listen to the Church Slavonic here.

Whether Latins should pray this version in their rosaries I don't know, but I would caution against combining the prayers.

Is there a "Church Approved" alternative text for the Hail Mary?

Perhaps this one fits the bill:

Hail Mary, full of sorrows, the Crucified is with thee: tearful art thou amongst women, and tearful is the fruit of thy womb, Jesus. Holy Mary, Mother of the Crucified, grant tears to us crucifiers of thy Son, now and at the hour of our death. Amen.

In the 19th century an alternative Hail Mary prayer, one that focused on Our Lady of Sorrows, became popular.

The Raccolta explains, “His Holiness Pope Pius IX., by a decree…of Dec. 23, 1847 [encouraged the faithful to] say with contrite heart the following prayer in honor of the most holy Virgin in her desolation.”

The prayer meditates at the sorrowful heart of Mary and how Jesus’ crucifixion caused her much anguish.

An alternative Hail Mary to Our Lady of Sorrows

I would like to draw some attention to the historical development of the Hail Mary.

For many centuries the the Hail Mary comprised simply of the Angelic Salutation of the Angel Gabriel to Mary herself.

And the angel being come in, said unto her: Hail, full of grace, the Lord is with thee: blessed art thou among women. - Luke 1:28

And she cried out with a loud voice, and said: Blessed art thou among women, and blessed is the fruit of thy womb. - Luke 1:42

Hail Mary, Full of Grace, the Lord is with thee. Blessed art thou among women, and blessed is the fruit of thy womb, Jesus.

The fact is that last part of the Hail Mary was added to the original Hail Mary during the Black Plague.

The “Hail Mary” prayer that Christians have been praying for centuries is composed of two main parts. The first part of the prayer is derived from the Annunciation, when the angel Gabriel greeted Mary by saying, “Hail, full of grace, the Lord is with you!” (Luke 1:28) The next part of the prayer is taken from the Visitation, when Elizabeth greeted Mary with the words, “Blessed are you among women, and blessed is the fruit of your womb!” (Luke 1:42)

At first the prayer was known as the “Salutation of the Blessed Virgin,” and only consisted of the two verses joined together. However, during the Black Plague (also known as the “Black Death”) the prayer was further developed and a second part was added to it.

This second part (“Holy Mary, Mother of God, pray for us sinners now, and at the hour of our death”) is believed by many to have been added during the plague to ask for the Blessed Mother’s protection from the fatal disease.

Venerable Fulton J. Sheen explains this origin in his book The World’s First Love.

Since it seizes upon the two decisive moments of life: “now” and “at the hour of our death,” it suggests the spontaneous outcry of people in a great calamity. The Black Death, which ravaged all Europe and wiped out one-third of its population, prompted the faithful to cry out to the Mother of Our Lord to protect them at a time when the present moment and death were almost one.

How the Black Plague changed the “Hail Mary” prayer

The Hail Mary in French does not conclude with the word Amen, although some French do. While I was living in France, we all said Ainsi soit-il in lieu of Amen.

Another point which I truly love about the Hail Mary “en français” is that they add the words poor sinners (pauvres pêcheurs) to their Ave Maria.

For those who wanted prayers: here's the "Hail Mary.

Je vous salue, Marie, pleine de grâce. Le Seigneur est avec vous. Vous êtes bénie entre toutes les femmes, et Jésus, le fruit de vos entrailles, est béni. Sainte Marie, mère de Dieu, priez pour nous pauvres pêcheurs, maintenant et à l'heure de notre mort. Ainsi soit-il. - Je vous salue Marie

There is an alternative Hail Mary in French but I am unsure how popular it is or if this version has been approved or not:

“Je vous salue Marie, comblée de grâce, Le Seigneur est avec vous, Vous êtes bénie entre toutes les femmes, Et Jésus, le fruit de vos entrailles, est béni. Sainte Marie, Mère de Dieu, Priez pour nous, pauvres pécheurs, Maintenant, et à l'heure de notre mort. Amen.” - Hail Mary in French

There exists other variations of the Hail Mary:

Greek tradition:

The Hail Mary prayer of the Eastern Orthodox Church and Eastern Catholic Churches is translated as:

"Mother of God and Virgin, rejoice, Mary full of grace, the Lord is with thee. Blessed art thou amongst women, and blessed is the fruit of thy womb, for thou hast given birth to the Savior of our souls."

Variant Slavonic versions There exist two variant versions in Church Slavonic:

Theotokos Virgin, rejoice, (or, Rejoice, O Virgin Theotokos) Mary full of grace, the Lord is with thee. Blessed art thou among women, and blessed is the fruit of thy womb, for thou hast borne Christ the Savior, the Deliverer of our souls.

Theotokos Virgin, rejoice, (or, Rejoice, O Virgin Theotokos) Mary full of grace, The Lord is with thee. Blessed art thou among women, and blessed is the fruit of thy womb, for thou hast borne the Savior of our souls

The first is the older, and remains in use by the Old Believers as well as those who follow the Ruthenian recension (among them the Ukrainian Greek-Catholic Church and the Ruthenian Catholic Church). The second appeared in 1656 under the liturgical reforms of Patriarch Nikon of Moscow, and is in use by the Russian Orthodox Church, the Serbian Orthodox Church, the Bulgarian Orthodox Church and the Ukrainian Orthodox Church).

Hail Mary