IIRC, Carter was slightly ahead in mid-October before the debate.
The company I worked for at the time had a Japanese engineer visiting for work on a big upcoming project and he watched the debate with us. He was riveted to the TV set and when Carter mentioned his daughter, he blurted out something like, "I'm not familiar with your election process, but I think that guy just lost the election!".
A couple of years later, he and I were down in Argentina starting up the project and some of the local engineers were (discreetly) complaining about their government. They said that the U.S. was lucky to have Reagan and not as many Socialists as Argentina did. Ken (the Japanese guy) replied, "They do have them, they just call them Democrats!"
Ronald Reagan and Maggie Thatcher were well thought of down there by the more educated people we associated with, and this was after the Falklands War. Prince Andrew (a.k.a. "Randy Andy") was the hero of quite a few Argentine women.