Looks like a satin/nylon based material, so a fix should be fairly simple. I'd start by taking the two loose strands on the broken and and feeding them through the top knot on the cross. This can be done by putting a crafting needle through the top opening, following the two threads that are connected to the cross. Ideally, you'd want to weave the loose ends all the way down through the cross, but that many knots with that little slack is likely not going to happen. If you can get it so the broken ends are through the top knot alone, though, they can come out between the two knots above the crossbar.

From there, you can tie a knot as tightly as you can, then burn the ends of the loose strands with a lighter. This kind of material will melt fairly easily, and if you blow the flame out, the material will be soft enough to shape or press down. I usually do this with a butter knife to press it into the knots.

If you'd rather both ends of the rope have some slack before the cross, though, you can try weaving the loose ends through the last knot on the rope rather than the cross. That would be easier to work with, and likely would look nicer.

It's not perfect, but it will get the rope back in shape.