When will you be visiting? Where will you be renting the canoe? Will you have a vehicle/trailer capable of transporting the canoe?
The Verde River is an excellent source for avian life in Arizona, but the water flow is quite variable, and it's not flatwater.
There are several lakes that may be more suitable for your desires depending on the time of year of your visit. Upper and Lower Lake Mary near flagstaff can be quite scenic, as can Ashurst Lake near there as well, though Ashurst is considerably smaller. Blue Ridge Reservoir is a dammed creek in a winding canyon, not very wide, but a few miles long. The Rim Lakes (Willow Springs, Bear Canyon, Woods Canyon) are smaller and tend to be crowded in summer, limiting the amount of wildlife you might encounter. They are also a bit further from the Cottonwood/Sedona/Flagstaff area.
http://www.fs.fed.us/r3/coconino/recrea ... shtml#boat
http://www.fs.fed.us/r3/coconino/recrea ... boat.shtml
There are a couple of smaller lakes near Prescott (Watson, Goldwater, Lynx).
http://www.fs.fed.us/r3/prescott/recrea ... lake.shtml
If you venture south to the lower desert you will find large reservoir lakes: Pleasant, Canyon, Saguaro, Apache, Roosevelt, and Bartlett. Horseshoe is full in the spring but often empty the rest of the year.
A good source for additional information is the Arizona Game and Fish site which has boating requirements as well links for lake levels and fishing reports. http://www.azgfd.gov/outdoor_recreation/boating.shtml
(Hopefully the link to the boating map will be "updated" soon. It's not currently loading).