My mother had a franco belge stove. It gave her many years of good service.
Hers was vented into the fireplace. At first the pipe was put in to just above the smoke shelf. A few years later the fireplace was closed off with a piece of stainless steel below the smoke shelf and the pipe was then run to just below the smoke shelf. Both methods worked fine. If anything, there was too much draft. She lives in a ranch house with an open field in front of her. When the wind screamed across the field and hit her house the draft was too much. This was fixed by having two manual dampers installed in the pipe.
I think running the pipe all the way up to the top of the chimney is a waste of time and money (assuming the chimney is in good conditon).