Im fixing up an old Peugeot and discovered that the steer tube is slightly bent and rubbing on the inside of the head tube. I want to replace the fork with another Peugeot fork that has a slightly shorter steerer tube. My question is how will that affect the stem? The height difference might be 10 mm, I'm not sure because I don't have the fork in my possesion yet.

Thanks in advance for answers that stay on point
Ground Hog

The primary problem you will likely encounter will not be with stem height, but with your ability to fit all components of the headset on to the new fork.

With threaded headsets there's very little latitude in fork steerer length. The steerer has to reach into the locknut which has about 8mm of thread, so if you plan to engage at least 4 threads, you only have 3mm to play with.

If your old fork and headset have lots of spacers you plan to remove, or if you're replacing the headset with one have a lower stack height you can shorten the fork accordingly. Otherwise you need to replace with an almost identical fork.

BTW- French made Peugeots use French thread headsets, and a smaller diameter quill stem than standatd (BSC or ISO) so check yours before shopping for replacements, lest you end up spending more chasing compatibility. Fork, then headset, then stem then handlebars.

If anything you can always get a fork with a larger steer tube and just cut it down to the proper height. I've made a tall bike(two frames welded together) and the fork i made for the bike was a bit too short in result i couldnt use the bearings, it worked, but it is really really not ideal.