Hi and welcome to the forum.

When I moved from the US to Germany, I used the same moving company that my employer had used when I had a one-year assignment in the UK. Unfortunately, that was 15 years ago and I was moving both times from California, so the same company may not even be around anymore. If you have any large international employers in the area, you may want to ask who they use for international moves.

The big US moving companies, United and Allied (probably some of the others, too), have international affiliates, and in fact that's what you're going to have to rely on. Check the Yellow Pages to see if any movers in your area advertise "international moves" and then get estimates and compare. It's not just a matter of the lowest bid, but also you sense of the company and how they operate.

It generally takes a month or so for your stuff to arrive from the East Coast of the US, longer from the Midwest or West Coast, and when it does, it then has to clear customs, which takes a day or two. If you're going to move yourselves and then your belongings, it might be better to store things in the US (where you have friends or family who could run interference for you should problems develop).

The moving company will have their affiliates on the other end of the transaction to clear your shipment through customs and then take it to Beaune. Your experience on the receiving end depends entirely on the affiliate.

Basically I'd say to stick to the larger, national companies and ask lots of questions when you get your estimates done.
Cheers,
Bev