A blessed Nativity / Theophany season to all!
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This book is not regarded as canonical by the Orthodox church. It does contain the story of the Nativity of the Theotokos, in a manner similiar to that preserved by Holy Tradition, and that story you can read by reading the kontakion and other hymns sung on that feast day, which I believe are in the Festal Menaion as translated by Metropolitan Kallistos Ware and Mother Mary. I can confirm that later today once I am back home, where I have a copy. The Orthodox service book by Fr. Seraphim Nasser also would contain the propers for that liturgy. Additionally, other aspects of the story are celebrated on the feast of the Presentation of the Theotokos, on February 2nd, known in the Western liturgical tradition as Candlemass. That should also be in the Festal Menaion, and in the “Nasser Five Pounder.”
There is also an app, called the Coptic Reader app, which costs money to download all the content for, although you might not need all of of it; it features the hymns sung for these feasts, and also a description of them, from the Coptic liturgy, particularly in the Psalmody and in the Synaxarion.
The Malankara Orthodox Syrian Church has gradually been translating the Syriac Rite book of propers for feasts, called the Fanqitho, and you might be able to find translations of the liturgy for those two services on their website; again, I can look it up for you. That material, if it is accessible, would also likely be beautiful and of very high quality.
I don’t think the relevant services from the Armenian or Ethiopian churches have been translated into English, unfortunately.
I can also attempt to find a good translation of the Protoevangelion of James, but again, I advise against it, as it is not canonical; the hymns of the Eastern and Oriental Orthodox churches contain what we actually believe about the events depicted in the Protoevangelion, whereas the Protoevangelion is a non-canonical work, which at best, was a work of devotional literature, but we don’t really know. You should read the hymns first, at any rate.
Finally, the Breviary and the Missal of the old Latin Rite of the Roman Catholic church is online, and you could round things out by reading the hymns they sing on those two occasions. I can dig up the URLs for you if interested. Their hymns are probably accurate, but I would trust the Byzantine and OO hymnody more.