Today at about 18:00 I was looking for Venus near the moon and I saw a short bright line. I thought that maybe I was seeing Venus' crescent but it was perpendicular to the crescent of the moon. I then noticed Venus very close to the moon and realised that the line is Jupiter. I can confirm the location was Jupiter in Stellarium, and I can confirm in Stellarium that the moons are in fact aligned in the direction that I saw the line. Is it possible that I caught a glimpse of the Jupiter-moons system as a line and not a point source?
The Galilean moons are (barely) bright enough to be seen with the naked eye, but they're so close to the much brighter Jupiter that seeing them is at best very difficult (but easy with even low-powered binoculars). Jupiter is not currently at opposition (the closest it gets to Earth), so that's not ideal.
I've never seen them without binoculars or a telescope, but someone with very good eyes in excellent seeing conditions might be able to make them out. And the OP didn't see them individually, just "a bright line".
Try again if you get another opportunity. If you see the "bright line", try rotating your head. If the line rotates along with your head, you're seeing some other phenomenon, perhaps an irregularity in your eyes, or a reflection in your glasses or contact lenses if you wear them. If it doesn't rotate, I'd say there's a good chance you're really seeing the Galilean moons.
Another test would be to repeat the observation when all the moons are on the same side of Jupiter.
Just to gauge your eyesight, how many Pleiades are you able to see without binoculars or a telescope?
(And in case anyone is wondering, Jupiter's rings are not visible with the naked eye; they weren't even discovered until the Voyager 1 flyby in 1979.)