It seems with all of the rain we've had in LA that a small portion of
the stucco around one of my front windows has cracked and peeled off.

It looks like some framing was created by using styrofoam around the
window and then stucco'ing over the styrofoam to make a frame. The
stucco was then painted white to contrast with the rest of the yellow
stucco.

What would be the best way to repair? Use some stucco patch and then
repaint the frame white?

Styrofoam seems like a strange material to use to create the frame.
Does this seem wierd? Maybe it is a good material because it doesn't
retain water.