In Chantelise, I'm assuming that everything marked [Treasure] in that I pick up is just junk that I can sell back to the store for cash. Is there any other use for Treasure items other than vendoring? I don't want to accidentally sell something that I may need for a puzzle or a quest somewhere later along the line.
The purpose of all items marked "Treasure" is to be sold. Keep in mind that the more you sell stuff, the less money you'll get for it, but it does flat-line eventually.
Starting in Chapter 2, you'll get access to another shop, which sells a small inventory. However, as you sell certain pieces of treasure, new items can be unlocked to purchase there. It doesn't matter whether you sell the items to Aira or to this shop, both will contribute towards unlocking new items. Note that all of these require specifically the kind of treasures dropped by enemies, rather than things such as golden idols.