We need to buy car insurance for a French car we just bought yesterday. We need a company that specializes in working with expats.
I am American, here on a long-stay visitor visa, but with plans to stay indefinitely. Groupama required me to have a French Driver's License, and to have all my no claims letters to be translated into French by a certified translator. They also required my lease be translated into French since I do have an EDF account (my electric is included in my rent). And a bunch of other stuff. Grrr.... So instead, we went with AON Expat, it took only 30 minutes and we had the printable insurance card in our Inbox!
I bought and insured my French car a few months ago through Axa. You need your carte grise etc from the garage you bought it from plus your driving licence and any no claims certificate you might have (I'm English but had a Maltese no claims certificate - no problem, they're all acceptable). Unless there's a specific reason that wasn't mentioned in your post, that's all you need. The insurance companies don't care what nationality you are as such, it's the car they're interested in.