I have bought an 80ies (?) Vicini vintage road bike that I've mostly used on flat terrain so that I haven't used the smallest gear until recently. I found out that the chain rattles against the front derailleur in the smallest gear. I've loosened the lower adjustment screw as far as it goes and put all the tension from the shifting cable but it still rattles. The FD is installed at the correct height and parallel to the chain. The only possible explanation I can imagine is that the BB isn't wide enough. It is an old Shimano 105 chainset with frame downtube shifters.
Assuming you haven’t done so, I’d check that the derailleur moves freely and isn’t seized or gunked, preventing it springing inboard up against the low limit screw. You can peak at the screw tip to check.
Drip some oil in the pivot points and maybe spray light lube carefully on the mechanism, then exercise the FD manually with your hands a number of times to make sure it is moving freely. (No chain movement or cable tension).
It's worth measuring the chainline too and reporting back to ask if it’s in spec. for the B.B. spindle length possibility.
It might be that you can tweak the derailleur so that it isn't exactly parallel, but functions properly, i.e. no rubbing, shifts properly and doesn't drop the chain inboard or outboard from the chainrings. Try rotating the tail of the derailleur inboard just a little and see how you get on.
In addition to Swifty's suggestions, I would add a double check on cable tension. May as well release it at the anchor bolt, and with chain on large cog/small chainwheel, see how it looks then while you proceed with cleaning, lubing and exercising the pivot points.
This brings you to a point where it's like the beginning steps of a new derailleur install (low end of gears, cable not connected yet, and concerning yourself with proper mounting things like height above and parallelism to chainwheel).
Couple of other thoughts would be 1) as you're dealing with a friction shifting system in front, you can be more liberal with changing the angle of the front derailleur. 2) Be mindful that trimming of the front derailleur will be necessary. I've included a link to Sheldon Brown's article on front derailleurs. His writings are very good, and believe me, you'll come away with knowledge and lots of leeway to fix your troubles-- including breaking out the angle grinder and taking care of that chain rubbing problem at your front mech. Lol. https://www.sheldonbrown.com/front-derailers.html