I can't believe I hadn't been here before. This place speaks "Mel C."!
Not only does it meet my "open early on Sunday" requirement, the Pain Perdu is the best thing I've ever eaten for brunch! Love the décor/ambience of this quaint café. Service was fantastic. I even got some goodies to go (various croissants) and they were all amazingly good. Keep in mind I've had croissants in Paris, so I feel very qualified*.
Make sure you get there early enough to get some Pain Perdu. Once they're sold out for the day, that's it!
*not officially qualified