For normal (non-Airbnb type) furnished and unfurnished apartments in France - those involving a lease- renter's insurance is mandatory and will cover jewelry if you so choose. It isn't expensive- we pay something like $300/yr. with Lemonade.
You can get an idea of costs by fooling around with a comparator like les Furets.

https://www.lesfurets.com/

 

Insurance in France is kind of funny. Many sorts of insurance (like renters insurance) are actually a form of liability insurance to protect you from claims based on damages you are deemed to have caused (or that you are considered responsible for). But both renters and household insurance also include provision for insuring you personal belongings. Jewelry may or may not have to be separately declared when you take the insurance. Best to ask when you're setting up your policy.

 

Yes, when we took out both our rental contracts and home owner contracts the insurance company asked about any objects of value (be they jewelry, electronics, etc.). The basic policies had a cap on how much they would cover of these types of objects. If you wanted more coverage, you could get it, you just had to itemize the objects in question.

 

Thanks everyone! I ended up getting a valuable property policy from USAA along with a renter's policy and am very pleased. It covers our belongings both in our french lodgings and in our US storage unit. If you have access to USAA they are super used to helping families moving overseas (since they focus on military families) - setting it up was a breeze!