I wasn’t sure what to call this Spider-Woman because she was only in a single story of a french publication in 1981, and her identity was never revealed. The character probably isn’t French since the story takes place in New York City, but I guess there’s also nothing saying she isn’t French. But that’s all besides the point.
This Spider-Woman is a member of the Woman’s Liberation Movement, or WLM. In the story, when Spider-Man starts getting lots of press about saving the day, the President of the WLM wants to prove that a woman can be just as heroic as a man, and so she gives a costume to their most athletic member, whose name, as I said before, is never revealed to us. The President of the WLM also plans to take plenty of pictures of Spider-Woman in action and sell them to the Daily Bugle to make sure the world sees that women can be strong too. Their plan works, and soon Spider-Woman is all everyone is talking about.
Without any super powers at all, she saves people from burning buildings, fights criminals, and generally fights crime around the city. She is shown climbing drainage pipes to scale buildings and swing from them into windows. At one point she even saves a man from a car that has just driven off the bridge into the East River and swimming with him to safety.
Eventually Spider-Man finds and confronts Spider-Woman, and after witnessing her save a baby from falling out of a window, asks her about her costume. She explains the situation and her reasoning, but Spider-Man simply says that despite her bravery and fitness level, she will just get herself into trouble without any real superpowers.
Later when Spider-Man goes to confront Spider-Woman again, the President of the WLM, who is trying to take a picture of them, falls from the side of the building and her coat catches on a nail. Spider-Woman is unable to reach her, and so she asks Spider-Man to use his powers to save her. He easily wall-crawls over and saves her, and then basically says “I told you so” regarding needing powers to do the job.
What a jerk.