That's a sweet Gitane.
Glad you fixed it!
Just one more data point / anecdote: I had a Continental Gatorskin that showed exactly what you've got in your video. I could not get that to be any better after deflating / reseating / inflating repeatedly. The bead and tube were seated just fine in the wheel, so I finally accepted it must be a messed up tyre, and I bit the bullet and just bought another one, which worked perfectly. Sometimes you can just have bad luck and get a bad tyre.