there are no actual breakfast restaurants open in the parks at all. There are cafes where you could get a pastry and a hot drink though.
Outside the park, you have Cafe Mickey which is a character breakfast buffet (its expensive though, 24 euros per person, adult or child).
You can also have the full breakfast buffet (hot and cold items and lots of variety) at the
Disneyland Hotel or Hotel New York. You don't have to be a guest at either of these hotels to have breakfast there. We have reviews of the Disneyland Hotel breakfast in the restaurant review threads, its currently around 14 euros per adult, 6 euros per child. The Hotel New York version is slightly cheaper, around 11 euros per adult, 4 or 5 euros per child.
There is also McDonalds in the Village, Earl of Sandwich, and Starbucks which open in the morning (8am or 8.30am I believe).
Annettes Diner opens at 9am I think, and has an American-style breakfast plate available until 1pm.