Store is the most common and general term.

Jalousie is used to refer to a specific type of store. A more common synonym would be persienne. But as you seem to guess, the word jalousie also means “jealousy” and that will be the first meaning any native speaker will think about if you mention this word.

In my experience, jalousie is used to refer to a store only if you want to be very specific about the exact type eg if you will talk to a decorator. Most native speakers will use the word store, and I would not be surprised if many of them have even never heard jalousie in another meaning than “jealousy”, hence the surprise your using this word may cause.

The word jalousie is still used in the region of Lyon.
This is not only a linguistic regionalism. A persienne is a persienne (see https://fr.wikipedia.org/wiki/Persienne) but when you can play with the orientation of the lames of the persienne or retract them, then it is called a store vénitien or … a jalousie in Lyon ! (https://fr.wikipedia.org/wiki/Jalousie_(architecture)).