It's just a falsobordone, and the same one for all 3 propers. Now, WHICH falsobordone could be difficult, as most of us don't use them much, alas. This one sounds like it may be comparatively new (within the last century). Is this Portugal, or Brazil? I would make a difference in where to look, I suspect the organ introductions are improvised. Otherwise, it's conceivable that somebody could transcribe from the recording, though it would mean listening to that choir, which is not the best.

The idea of setting the Propers to a falsobordone is a good one, and if we can't find the specific one, maybe you can find another that you like. It's basically the classy version of the Rossini Propers. As you've probably noticed, there aren't many composed settings of the Proper for the Wedding Mass, and almost none from the Renaissance. I assume you have considered the chant; why have you decided against it?

Here's the Introit Deus Israel conjungat vos, set as close as my ears could hear it, to the falsobordone chant in the video. I was swept away by the beautiful simplicity and simple beauty of this chant ... in truth, I have been reduced to tears of joy by this music.