I wanted to give you my experience with a baby and stroller. This was my wife, 15 month old and me travelling BOS-CDG-DXB and DXB-CDG-MSP in coach.

For the BOS-CDG flight, they initially wanted to gate check it, but after a brief protest, they agreed to let us take it on board and a FA put it in the business closet. This flight was almost full, but we were lucky that the crew was very nice and moved someone so we could have a free seat for our daughter. Having the stroller in CDG was a godsend as we had a long connection there. It was difficult on arrival though because we deboarded with airstairs into the rain (but that's an unrelated AF deficiency).

For the CDG-DXB flight, they insisted on gate checking the stroller to baggage claim. We protested but to no avail. The long long walk from the plane, through immigration to the baggage claim in DXB was no fun at all. I don't think there was another option though. The ground handling in CDG is incredibly unhelpful.

For DXB-CDG they tried to make us check the stroller at checkin. We protested that we need the stroller for our connection. After some consultation, the checkin agent rooted around and found a special "gate check" sticker (which said KLM and not AF on it) that she stuck on the stroller and said that they would give it back to us in CDG after checking it planeside at DXB. At planeside in DXB I confirmed this with the person handling strollers on the tarmac, and pointed to this sticker. Trying to organize this special gate check was a bad idea. When we arrived in CDG the person on the jetway was adamant that we were not getting our stroller back in CDG and that it would be checked to our final destination. Because our first flight was late, we didn't have time to argue and ran to make the connection.

On arrival in MSP, the stroller did not come out in baggage claim. They delivered it to our hotel there the following evening.

I think the moral of the story is to push hard to get the stroller on the plane with you but to have a backup plan if they don't let you. Or to not fly AF with small children.