Benny's is open at 8 am and it's in your area.(the website for the French Baker doesn't give hours!) Baker Street Cafe may be good (I've never been) but it is really is quite out of your way.
Another option in the downtown core, but not in the Market, is Sconewitch at Albert and Lyon Street. They have wonderful scones as well as breakfast sandwiches (on scones) and it opens at 7 am on weekdays, 8 am on Saturday. It is a little bit out of your way - about 2-3 km - but I've never been disappointed.
There's another one at 35 Beechwood that might be closer but I don't know the area so can't reccommend it.
Baker Street Cafe
385 Rd Richmond, Ottawa, ON K2A0E7, CA