As a longer term sustainable option, but one that would require time and effort to become established is to put large heavy, sturdy pots/tubs at close intervals along the frame along the side of the terrace. Fill the tubs with soil an plant vines, possibly grapes. The filled tubs need to be heavy to remain in place during extremely bad weather. Also, the tubs need to be large enough for the plants to develop a good root system.
A few examples of the types of pots/tubs to consider.
Train the vines to attach themselves to the frame. Stainless steel wire or cable may need to be hung between the posts of the frame to support the vines. Narrow diameter holes could be drilled through the frame posts and the cable threaded through the holes. Something similar to this,
During winter the bare branches of the vines will be visible but during summer the vines and the frame will be shaded by the leaves of the vines.
It will become messy for a few weeks in autumn when the leaves fall off and some "garden" maintenance will be required to prune dead or wayward branches, but nothing too demanding.
If possible attach a solar powered automatic drip watering system and possibly incorporate a liquid fertilizer system in the watering system during the vine growing period - early Spring to late Summer.
To help conserve soil moisture in the tubs put a thick layer of mulch as the top layer in the tubs.
As to your more pressing need. The bamboo or reed mats will be easy but they will need to be replace more often because they are made of organic material which will degrade quickly.
Woven polyethylene fabric will last for 10 to 15 years, but it's plastic and end disposal needs to be considered carefully, particularly since you live on a island.
Good quality canvas will last for up to 15 years before it needs replacing It is made from a natural material and final disposal will be less of a problem than polyethylene fabric and will have a lesser environmental impact.