It is fake. That eagle weights 12 lbs at most no way can it lift something much heavier then it. That is not a fresh new born your talking at least 20lbs, no way. I can see a cat or a small dog but no way it picks up a kid old enough to sit up.
There was a report on the "Today" show this morning on this video. They showed the kids in Montreal that produced it. Among the things pointed out...at one point the eagle has his wing cut in half in the video for a few frames...then it reappears whole. Also, the eagle as he swoops down does not cast a shadow...then one appears.
They used really nice computer animation to create this...and apparently have done other commercial work. (There is a video out there of people seemingly flying like birds over Manhattan).