Whack the seat stays the direction you need them to go, at the bridge. It's not uncommon for the seat stays to be a small amount out of alignment with the dropouts in near perfect alignment. The depth of 1 thread is enough of a difference at the axle to make a significant difference at the seat stays, so the dropouts could look and measure aligned. Actually before hammering on the seat stays, measure, measure, measure to see how far out of alignment they are at the bridge. I'd make sure the seatpost and head tube are in alignment, stick the bare frame on a few 2x4s to keep it off the ground and have a whack with a deadblow hammer right at the seatstay bridge. Then measure everything. You could keep an axle clamped in your dropouts to ensure you don't put those out of alignment and create another confounding factor.

It's an old bike. Things happen along the long lifetime of the bike. I wouldn't expect that it was made that way. It might be that it was "fixed" that way by someone after something worse happened. A slight bend in one of the stays from something or someone falling on it while it was laying on the ground might give enough to have it out of kilter.

How well does the rear axle fit in the slot of the drop out? If there is side to side play in the axle without the QR or nut being tightened, then does that account for the off-center between the seat stays? If so is the slot wallowed out? a crack developing in the radius of the slot, or the axle undersized?

You said you made something to check if the drops are parallel. They might be parallel, and the frame bent somewhere else. Still seems like if you have the drops held parallel to each other and you have that axis between them horizontal to the ground, then you would see if the frame leans one way or not. And if it does, then you can try to bend it back. Even if it bends something else.

It is after all an old frame. We don't have any frame builders anywhere near me that I'm aware of. Perhaps there might be some near you. If there are some that do it professionally for money there might be some that do it as a hobby. Perhaps you can find one of those willing to check out the frame alignment and fix it just for the sake of saving history. But for a one off thing, it'll take time. And time is money usually.

I just saw a video of someone aligning a bmx frame with a hammer. That frame must have been made out of really thick tubing, because it didn't seem to dent the tubing. But unless you see that one of the stays is slightly bent, you could bend the long seat stay a little. I'm not sure I would try it. Moving one of the dropouts by un-brazing and re-brazing is an option if you are repainting, but it doesn't seem like it would be worth it on a beater.

...it does show up occasionally. I have one bicycle, a Zeus competition from the '70's, that was misassembled in this way (one shorter seat stay...or I guess one longer one, depending on your perspective.)
On mine, I managed to find one spot, moving the rear wheel backward and and forward in the horizontal dropouts (which are not both strictly horizontal), where the wheel rim centers between the seat stays.

If you are certain this is the problem, with a cheap, mild steel frame like the one you describe, you can very carefully bend (curve) the longer seat stay, and improve your circumstances. But as advised above, make sure that this is the problem. Try carefully measuring the length of each seat stay, from where it contacts the seat tube, to where it ends at the dropout. Use similar identical starting and ending points on both sides. That might help in your diagnosis.

You're telling someone to possibly ruin their frame. Most non-Reynolds Peugeot tubing is notoriously soft, and will dent easily. add to that the fact that you are advising moving TWO tubes at once with side blows to ONE tube... wow.. Bad idea.
PS.. the length of tubing that is most likely bent is the length BELOW the bridge, since the bridge creates a triangle that doesn't want to be moved.

:notamused:

and i'm assuming it's an old UO-8 or one of the overweight MTB variants... i went to thinking it should be "horizontal" when i read "peugeot"... :rolleyes:

and that title has now been edited. ;)

Bikes sharing a garage with cars can get a little sideways nudge from a bumper or door without anyone noticing.

Meanwhile there are folks here suggesting more drastic (as well as less drastic) possible remedies, yourself included.
The stays of the bike in question are HiTen, just like the stays of most bicycles out there. Yes, application of force to move the triangle at the bridge could dent the stay, but if the deformation in the frame which has caused the short stay happened at the seat collar, there is no other remedy. Granted, as this is a mixte frame, it will be more difficult to repair, but it's not impossible. It's possible that the seat tube is bent at the level of the brake bridge. The noodle-like stays of a UO-8 can take it, especially if the force of the blow were spread out using the end of a block of wood with a corresponding groove cut into it to match the radius of the tube. It doesn't take much force to bend it. Done carefully, this is an acceptable way to straighten a triangle misaligned in the vertical. It's been done to many bikes out there to fix this very problem.

This seems to be the only mention of the string test in this thread.

The OP should look at the first two RJ The Bike Guy videos on this page.

Or to learn more faster without listening to the annoying guy, refer to Sheldon's page on frame repair.

Yes and no.

Back in post nine, I described two simple 5 minute diagnostic tests. One for an off plumb rear wheel, and the other, similar but different than the string test for a bent frame.

Later in post 15 I tried to be as clear as possible about the importance of taking measurements to identify the actual issue. Then once more later on.

Frame alignment issues can be complex, and it's easy to misidentify the exact nature. On this bike the dropouts may be at different heights, the frame misaligned at the axles, the frame twisted front to back, or the seatstays deflected at the bridge. Or a combination of two or all of the above, or something else.

To be clear, without being an asshat, anyone who bends, files, or otherwise makes a permanent change to a frame before properly identifying what's wrong is a moron and deserves whatever outcome results.

Measure twice, cut once is a maxim over 1,000 years old, and still valid today, ignore it at your own risk.