What type of blinds are these?

You are correct; it is just an unconstructed flat panel curtain that they have rolled up and tied. The ribbons (ties)run down both faces of the fabric & are anchored at the top. I would line with a slightly stiffened liner or interliner so they have some body when rolled. But if you are making these yourself, I would test a small swatch of the fabric for its body. Linen is notoriously limp. A linen blend or a synthetic linen would be better.