Sleeping Bag

I have found it still quite warm in September. At the higher elevations, there are blankets, though you may have to ask. You need some sort of "linens", so a sleep sack or sleeping bag is necessary. It will not be cold enough for a heavy one, though. Buen camino.

Keep in ming that depending on how much of the Camino Francés you are walking, it will be October before you finish. It can definitely get cold at night in October (though often it is still very nice). Many albergues have blankets but I don't recommend relying upon them. My suggestion would be to take a lightweight (summer-type) sleeping bag. Even if you only use it a few times, it can save you from a very, very uncomfortable night if temperatures happen to drop. It is no fun walking the next day on little-to-no sleep!

I always take a light weight summer sleeping bag and never regretted doing so.
Buen Camino! SY