OK. I used the second file.
There’s a bad spot on the path at the cursor. I used Eneroth Auto Weld to weld the edges of the path together but there’s a break in the welding here.
I redrew that section and welded it all before running Follow Me.
Due to the location of the path relative to the shape of the profile, there are places where the extrusion folds over itself which will need to be cleaned up but the Follow Me operation does complete as expected.
If you were to draw the path for the top corner of the profile instead of that bottom corner, you wouldn’t end up with the overlaps.
As an example, I moved the path you’d drawn up to the top of the triangle.
With Follow Me now there’s none of those overlaps as before.
Of course you can’t just move the path up because the base of the extrusion won’t be the shape you need. You’d need to create a new appropriate path instead. If it was flat you might be able to use Offset but that won’t work in this case so another method would be needed to draw the path.