It was my recollection that Lorelai and Rory didn't have a full breakfast (eggs, pancakes, sausage, etc.) on a weekday on a regular basis. Instead they had coffee and muffins, danishes and suchlike at Luke's. So they wouldn't need to be there at quite an ungodly hour. Of course, they really didn't need to be there at all. Coffee and baked goods could be managed at home.
I thought Michel was hired by Mia. Perhaps she was fond of his French snootiness :) In his defense he did do well with some customers, including - oddly enough - children. Also, he had formal hotel industry training so that may have come in handy in setting up and managing administrative systems and procedures. And if Lorelai was nutty enough to go into - and stay in - business with Sookie, then asking Michel to be an investor didn't seem like lunacy to me.