From what I remember the animation style was quite similar to The Mysterious Cities of Gold. I have a feeling it was a Japanese/French collaboration.
There was a city in a bubble, somewhat post-apocalyptic. From what I remember there were lots of robots and no people left in the city, only cyborgs.
It focused on the story of 4 people's escape, 2 children and woman and a man (a soldier). During their escape the man gets cut and it appears he's got robotic circuitry underneath his skin. Eventually, they get to the centre of the city to the robot control centre (?), only to find a boy controlling the robots. Eventually, they escape and the world outside the bubble is revealed to be full of life.
Sorry for the vague description, I have a feeling I may have added details from other movies I saw as a kid.