On a piece of cloth, a "fringe" is a decoration consisting of little threads or cords attached to the edge of the cloth.
This is a little mat, a "doily," that has a fringe on it:
Click on the link; let me know if you can see the image, I am never sure what people in foreign countries can or can't see.
The point is: a fringe is always at the very edge of the piece of cloth. It isn't really part of the main piece of cloth.
So, by extension, a political "fringe" consists of people who take extreme positions within a party--people whose positions are so extreme that, figuratively, they are hanging off the edge, and you can't quite say whether they are really a legitimate part of the party. It suggests a relatively small number of people, holding very extreme positions. It might be a shortening of the phrase "lunatic fringe."
"Is he a [political party name]?" "Oh, boy. I don't know. He says he is, but he's one of the crazies--part of the lunatic fringe."
So "fringe left" means the crazy, extreme part of the left wing, and "fringe right" means the crazy, extreme part of the right wing.
"Fringe" has a number of meanings and uses, but they all carry the idea of "extreme edge," "way out," "not sure it's even part of the main thing."
For example: "Where does he live?" "In Chester Village." "Where is that? I've never heard of it." "It's way, way out there." "On the outskirts of Zenith?" "Farther than that, it's way out on the fringe."
A famous arts festival, the Edinburgh Festival Fringe, began when some theatre groups couldn't get into the main venues of an arts festival, so they decided to perform anyway, in locations that were so far from Edinburgh that they were out on "the fringe."