Is there not a good reason for bleeding them all the way out, the way most people do here in the States? Just wondering--I'm sure they have a good reason for NOT bleeding them--it probably does make them very tender and/or juicy. The French do know a thing or two about good eats.
However, I will say this as well. France is not exactly known for its humane treatment of the animals it eats. It is, after all, the home of foie gras where a goose is painfully force fed several times a day with a pump to cause its internal organs to bloat and its body to become so large and ill that it can't move, all so someone in a fancy restaurant can eat a tiny little delicacy.
And suffocation doesn't sound like the quickest, most painless way of doing the deed. I'm not sure it's something I would try.
Sorry I'm not more help--perhaps someone here will have more insight. However, I do want to suggest that you put something in your title to indicate that you are talking about meat birds here--there are a lot of folks on this board who love their ducks as pets and might prefer not to read a thread about deliberately killing them--so it would be nice to warn them first.
Also, consider posting in the Meat Birds forum as well, as there are probably more experts on slaughtering methods there than here.
Good luck whatever you decide.