I suspect that I'm just shy from finding this. I saw a review of the game on YouTube a few years ago, which lauded it for its innovative mechanics, but I think commented that it was a bit too short, and the platforming a bit finicky (always a problem with 3d platformers). The game follows a young boy, I'm pretty sure in Europe, probably France, likely during World War II. His mother works in a bar, and I think his father is a soldier, so he's left in his room for long amounts of time. I think he can change places with the primary person that you control, a female acrobat, who can interact with shadows as if they were real objects, which led to much of the game being puzzles where you move objects and light sources to create the shadows necessary for her to get to a location to throw a switch to allow the boy to move.
I think the game's title may have started with a C, but all that's coming to mind is Control.