In the fifth century, the legal language of the Empire was still Latin, even though the liturgical language was Greek. Court business was conducted in Latin until the time of Heraclius I, who changed it to Greek in the interest of efficiency (the Empire being in crisis, and there being too few people who spoke Latin to conduct the necessary business of state).
Also, in the fifth century, marriage was still largely a civil institution within the Empire (and would remain so until the 9th century); it was only about this time that a Church marriage was accepted as evidence that a legal union existed, so we are really talking about two distinct acts here: the legally binding civil record, which creating mutual legal responsibilities, rights and obligations (regarding property, children, inheritance, etc.); and the sacramentally binding Church wedding.
The civil arrangements would have been conducted in Latin, according to the civil code. But a Church marriage ceremony carried out in Constantinople would have been conducted according to the Byzantine rite, and since it was a first marriage for both of them, there would have been a Crowning that looked much like that used in the Byzantine Churches today, except it would definitely have taken place within the context of a Divine Liturgy and been sealed with the Eucharist. And, being imperial, it would have been incredibly elaborate and ornate, and held within the Great Church of Hagia Sophia.
If it has been a second marriage for either, there would have been no Church wedding at all, because the Church did not have a "Rite of Remarriage" until the ninth century. Instead, their union would have been a simple civil ceremony, after which they would have presented themselves to the Church for reconciliation through prayer and fasting, and been barred from communion for two years. However, the Emperor being the Emperor, oikonomia would probably have been applied to reduce that period to a few months at most.
