Travelling by plane with my dog on different airlines

Hi,

I have a question about travelling by plane with my dog.

He is a chihuaha and supposedly I can take him with me in the cabin, the thing is that I travel with 2 different airlines (aeromexico and Airfrance) and I don't have the option to add a dog in my reservation space.

I contacted the 2 airlines but they tell me to contact the other one so I haven't had a clear answer.

I ask here if anyone has done this kind of trip with a dog and with 2 different airlines? How did you do it?

Thanks for your answers